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(((9 + 7) - (3 * 3)) + 4) =
((16 - (3 * 3)) + 4) = ((16 - 9) + 4) = (7 + 4) = 13 = 21 = 27 = 27 (1 - 13) = -12 = -11 (1 - 12) = -11 Earlier in the presentation cammer (7) of (9) + -12 + (
(16 - (3 * 3)) = (16 - 9) = 7 = 3 = 6 = 6 = 6 = 6 = 6 (16 + 9) = 25 = 39 = 58 VA = 6 + 56 = 58 D = 6 + 58 (6 + 58) = 65 (6 + 58) = 64 94 (
-1
-20
19
(((3 + 7) * (1 + 1)) * 8) =
((10 * (1 + 1)) * 8) = ((10 * 2) * 8) = (20 * 8) = 80 = 80) = 80 Let w(j) = 2*j - 5. Let g(k) = 8*k**2 - 9*k + 3. Let t(z) = -7
(10 * (1 + 1)) = (10 * 2) = 20 = 40 = 40 = 40 = 40 = 40 (2 * 10) = 20 = 20 = 40 = 40 = 40 (2 * 20) = 20 = 20 = 20 8 = 20 = 40 8 = 40 8 = 40
-2
-20
18
(((6 - 3) + 9) * ((5 * 8) * 7)) =
((3 + 9) * ((5 * 8) * 7)) = (13 * ((5 * 8) * 7)) = (13 * 28) = 84 = 84 = 1274 (84 = 84) = 234 = 234
(3 + 9) = 12 = 12 (6 + 9) = 21 (6 + 9) = 27 (6 + 9) = 27 33 (6 + 9) = 27 33 (6 + 9) = 27 33 (6 + 9) = 27 33 (6 + 9) = 27
-30
-62
32
(((4 * 2) + (3 + 3)) + 9) =
(8 + (3 + 3)) + 9 = (8 + 6) = 14 = 22 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 =
(8 + (3 + 3)) = (8 + 6) = 16 = 28 = 28 = 28 (16 + 28) = 48 = 56 16 (16 + 28) = 56 32 (16 - 56) = -40 -24 (16 - 56) = -48 -32 Some (16 +
-15
-20
5
(((2 - 1) * (2 + 2)) * 4) =
((1 * (2 + 2)) * 4) = ((1 * 4) * 4) = (6 * 4) = 24 (24 = 24) = 48 = 96 = 96) = 36 = 96 = 96 = 96) = 36 = 96 = 96) = 72 = 96) = 72) = 72) = 72) = 72) =
(1 * (2 + 2)) = (1 * 4) = 4 = 4 = 4 = 4 = 4 = 4 (1 * 4) = 4 = 4 = 4 6 1 1 1 1 1 1 3 1 1 1
-7
-20
13
(((3 - 9) + 4) + ((9 + 9) - 2)) =
((-6 + 4) + ((9 + 9) - 2)) = ((-6 + 4) + (18 - 2)) = (2 + (18 - 2)) = (2 + 16) = 18 = 20 = 18 8 (2 + 18) = 22 30 (2 + 18) = 22 32 (
((-6 + 4) + ((9 + 9) - 2)) = ((-6 + 4) + (18 - 2)) = (2 + (18 - 2)) = (2 + 16) =698 = 709 (698 = 709) = 709 (698 + 7) = 1011 ( 70 - 7) =
-3
-5
2
(((5 - 8) + (2 - 3)) * 2) =
((-3 + (2 - 3)) * 2) = ((-3 + -1) * 2) = (-5 * 2) = -10 = -20 = -20 (10*2) = -26 = -26 -26 (10*2) = -26 -26 follows from (10 + -26
(3 + (2 - 3)) = (3 + -1) = 2 = 1 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2) = 1 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2) = 1 = 2 = 2 = 2 = 2 =
-5
-25
20
(((6 - 4) - 5) - (3 - (4 - 8))) =
(2 - 5) = (3 - (3 - (4 - 8))) = (2 - (3 - -3)) = (2 - 6) = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 =
(2 - 5) - (3 - (4 - 8))) = (2 - 5) - (3 - -4)) = (2 - 5) - (3 - -4)) = (2 - 5) - (3 - -4)) = (2 - 5) - (3 - -4)) = -2 - (3 -
-35
-45
10
(((3 + 6) + (4 * 4)) - (8 + 5)) =
((9 + (4 * 4)) - (8 + 5)) = ((9 + 16) - (8 + 5)) = (21 - (8 + 5)) = (21 - 13) = 8 = 8 = 8 = 10 (8 + 9) = 17 = 27 (8 + 17) = 17 (17 + 17)
(9 + (4 * 4)) - (8 + 5) = (9 + 16) = 25 = 46 = 46 (25 + 46) = 57 = 79 = 119 (75 + 59) = 134 (75 - 59) = 26 (34 + 83) = 131 203 (75 + 59) = 202
-12
-48
36
(((7 - 1) * (6 + 4)) + ((8 + 8) + (5 - 4))) =
((6 * (6 + 4)) + ((8 + 8) + (5 - 4))) = ((6 * 10) + ((8 + 8) + (5 - 4))) = ((6 * 10) + (16 + (5 - 4))) = (630 + (16 + (5 - 4))) = (630 +
((6 * (6 + 4)) + ((8 + 8) + (5 - 4))) = (((6 * 10) + ((8 + 8) + (5 - 4))) = (6 + ((8 + 8) + (5 - 4))) = (6 + 16) = 22 = 26 = 26 = 22 (6 +
-34
-47
13
(((1 + 4) * (6 - 8)) - (6 * (4 + 8))) =
((5 * (6 - 8)) - (6 * (4 + 8))) = ((5 * -1) - (6 * (4 + 8))) = ((5 * -1) - (6 * 12)) = (-5 - (6 * 12)) = (-5 - 36) = -41 = -41 = - 41
(*4 * (6 - 8)) - (6 * (4 + 8)) = (*4 * 2) - (6 * 12)) = (8 * 2) - (12 * 12) = 64 - 84 = -8 = -8 = -8 = -8 = -8 = -8 = -8 = -8 = -8
-12
-43
31
(((1 - 1) - (8 - 9)) * ((4 + 3) - 2)) =
((0 - (8 - 9)) * ((4 + 3) - 2)) = ((0 - -1) * ((4 + 3) - 2)) = ((0 - -1) * (7 - 2)) = (1 * (7 - 2)) = (1 * 5) = 5 = 5 = 5 = 5 = 5 = 5
((0 - (8 - 9)) * ((4 + 3) - 2)) = ((0 - -1) * ((4 + 3) - 2)) = ((0 - -1) * seven) = (1 * seven) = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7
0
-22
22
(((2 + 6) * (6 * 6)) - 8) =
((8 * (6 * 6)) - 8) = ((8 * 36) - 8) = (288 - 8) = 260 = 248 = 248 = 248 = 248 (248 - 250) = -8 = -8 (8 + -8) = 0 0 (8 - 8) = 0 0 (0 -
((8 * (6 * 6)) - 8) = ((8 * 36) - 8) = (32 - 8) = 24 = 16
-1
-5
4
(((2 + 7) - (5 + 2)) * ((1 - 5) * (2 * 5))) =
((9 - (5 + 2)) * ((1 - 5) * (2 * 5))) = ((9 - 7) * ((1 - 5) * (2 * 5))) = ((9 - 7) * (4 * (2 * 5))) = ((9 - 7) * (4 * 10)) = (2 * (4 * 10
((9 - (5 + 2)) * ((1 - 5) * (2 * 5))) = ((9 - 7) * ((1 - 5) * (2 * 5))) = ((9 - 7) * (1 * (2 * 5))) = (9 * (1 * 5)) = (9 * 5) = 45
-20
-36
16
(((3 + 4) + (2 + 7)) - ((4 - 4) - 1)) =
((7 + (2 + 7)) - ((4 - 4) - 1)) = ((7 + 9) - ((4 - 4) - 1)) = (16 - ((4 - 4) - 1)) = (16 - 0) = 16 = 16 = 16 = 16 We can see from the graph that 7 - 0 =
(7 + (2 + 7)) = (7 + 9) = 16 = 27 (7 + 9) = 32 (7) = 32 (7) =32 (32) = 32 (32) = 32 (32) = 32 (32) = 32 (32) = 32 (32) =
-22
-77
55
(((5 + 5) * 1) + ((8 - 6) * 4)) =
(10 * 1) = 10 tells us that 5 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0
(10 * 1) = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10) = 10 = 10 = 10 = 10 = 10 = 10 = 10 = 10) = 10 = 10 = 10 = 10 = 10) = 10 = 10 = 10
-51
-55
4
(((8 - 4) - 2) - ((2 + 2) + (6 + 4))) =
((4 - 2) - ((2 + 2) + (6 + 4))) = ((4 - 2) - (4 + (6 + 4))) = ((4 - 2) - (4 + 10)) = (2 - (4 + 10)) = (2 - 14) = -12 = -12 = -12 = -12 = -
(4 - ((2 + 2) + (6 + 4))) = (4 - (4 + (6 + 4)) + (6 + 4)) = (4 - (4 + 8)) = (4 - 16) = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -
0
-39
39
(((8 + 4) * (4 * 7)) * ((5 + 9) * 3)) =
((12 * (4 * 7)) * ((5 + 9) * 3)) = ((12 * 28) * ((5 + 9) * 3)) = (96 * ((5 + 9) * 3)) = (96 * 13) = 144 = 216 = 268 (108 = 264) = 216 = 216 (108 = 216
((8 * (4 * 7)) * ((5 + 9) * 3)) = (((8 * 28) * ((5 + 9) * 3)))) = (((8 * 28) * (14 * 3)) = (((8 * 28) * 48)) = (112 (14 * 48)) = (112 (14 * 48)) =
-31
-38
7
(((2 * 6) * (2 * 8)) + 8) =
(12 * (2 * 8)) = (12 * 16) = 288 = 336 = 466 = 806 = 638 = 52 ((12 * 16) + (8 + 8)) = 288 = 336 = 416 = 52 56 (12 + (8 + 8)) = 288 = 336 = 52 56 (12 + 8)
(12 * (2 * 8)) = (12 * 16) = 96 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 = 144 =
-22
-23
1
(((9 * 2) + 7) + 8) =
(18 + 7) = 25 = 36 = 36 (18 + 7) = 55 = 51 (18 + 7) = 65 (27 - 55) = -42 -37 (18 + 51) = 63 75 (18 + 51) = 69 87 (18 - 69) = -42 - 27
(18 + 8) = 26.1 = 26.1 (18 + 8) = 36 = 44 52 (18 + 6) = 24 30 (18 + 18) = 36 42 (18 + 18) = 36 54 (18 + 18) = 36 36 (18 + 18) = 36
-13
-24
11
(((5 * 4) + (5 + 2)) + 6) =
((20 + (5 + 2)) + 6) = ((20 + 7) + 6) = (27 + 6) = 33 = 45 = 45 = 45 = 45 (27 - 6) = 21 = 21 = 21 (27 - 6) = 21 = 21
(20 + 6) = 26 + 26. 50 (20 + 6) = 26 + 26. 46 (20 + 26) = 46 66 (20 + 26) = 66 106 (20 + 26) = 66 10 (20 + 26) = 66 66 (20 + 26) = 66
0
-46
46
(((8 - 3) + 8) * ((7 * 8) - 6)) =
((5 + 8) * ((7 * 8) - 6)) = ((5 + 8) * 64) = (13 * 64) = 864 = 864. 864 ((5 + 8) * 64) = (13 * 64) = 864 = 864. 864 (13 * 64) = 8
(5 + 8) = 13 = 19 = 19 = 19 (5 + 8) = 21 = 26 = 27 (5 + 8) = 21 = 26 (5 + 8) = 21 (5 + 8) = 21 (5 + 8) = 21 (5 + 8) = 21
-41
-68
27
(((1 + 1) + 7) - (1 + (1 * 5))) =
(2 + (1 + (1 * 5))) = (2 + (1 + 5)) = (2 + 6) = 8 = 10 = 10 = 10 = 10 = 10 = 10 (2 + 4) = 8 = 8 = 8 = 8 (2 + 8) = 8 = 8 8 = 8 9 + 8 = 16
(2 + 7) = 9 = 11 = 11 = 11 = 11 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 =
-29
-58
29
(((5 - 4) - 8) + 7) =
(1 - 8) = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -
(1 + 7) = 8 = 8 = 8 = 8 (1 - 8) = -7 = -7 -7 (1 - 8) = -7 = -7 - 6 -7 (-11 - 8) = -17 - 21 - 12 - 12 - 12 - 12 -12
-14
-15
1
(((8 - 3) + 3) - 4) =
(5 - 3) = 2 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1 = 1) = (
(5 + 3) = 8 = 9 (5 + 3) = 8 = 8 1 (5 + 3) = 8 8 (5 + 8) = 13 17 (5 + 8) = 13 17 (5 + 8) = 13 13 (5 + 8) = 13 17 (5
-15
-20
5
(((6 * 4) * (2 * 9)) + ((2 - 7) * (7 * 7))) =
(24 * (2 * 9)) + ((2 - 7) * (7 * 7))) = (24 * 18) + ((2 - 7) * (7 * 7))) = (24 * 18) + (-6 * (7 * 7))) = (24 + (-6 * 7)) = (24 + -42) = -18 (
(24 * (2 * 9)) = (24 * 18) = 720 = 1126 = 1126 = 1126 (42 + 84) = 114 = 234 = 222 (42 + 54) = 171 = 333 (51 + 63) = 132 (51 + 63) = 162 (51 + 63) = 162 (
-38
-123
85
(((9 - 8) * 9) + 5) =
(1 * 9) + 5 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9) = (1 + 9) = 9 = 9 = 9 = 9) = 1 = 9 = 9 = 9 = 9) = 1 = 9 = 9
(1 * 9) = 9 = 9 (1 * 9) = 9 = 9 (9 + 9) = 18 = 27 (9 + 9) = 27 (18 + 27) = 45 69 (18 + 18) = 57 81 (18 + 18) = 57 99 (9 + 9)
-10
-19
9
(((1 * 4) * (4 * 3)) * 2) =
((4 * (4 * 3)) * 2) = ((4 * 12) * 2) = (48 * 2) = 96 = 192 = 264 = 576 (96 * 2) = 192 = 264 = 264 = 264 (96 * 2) = 192 = 264 = 264 4 (96 = 208) = 264 = 264
(4 * (4 * 3)) = (4 * 6) = 24 = 12 + 24 = 36 (4 * 6) = 48 = 48 + 24 = 48 (48) = 48 48 (48) = 48 24 (48) = 48 48 (48) = 48 48 8 8
0
-28
28
(((5 * 6) + 7) - ((4 + 4) * 2)) =
(15 + (4 + 4)) = (15 + 8) = 23 = 23 = 23 = 23 = 23 (23 + 23) = 43 = 78 = 103 (23 - 78) = -55 (59 - 75) = -34 (14 - 49) = -35 (84 - 85
(30 + 7) = 37 = 58 = 58 = 58 = 58 twitter.com/i/7 twitter.com/i/7 twitter.com/i/7 twitter.com/i/7 twitter.com/i/7 twitter.com/i/7 twitter.
-50
-60
10
(((6 - 3) * 6) - (6 * 3)) =
((3 * 6) - (6 * 3)) = (18 - (6 * 3)) = (18 - 18) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 =
(3 * 6) = 18. 6 (3 * 6) = 18. 18 What (3 * 6) = 18 18 (3 * 6) = 18 18 (3 * 6) = 18 27 ((6 - 6) + 18) = 18 18 (3*6) = 18
-8
-39
31
(((2 * 3) + (7 - 9)) - ((2 * 7) * 4)) =
((6 + (7 - 9)) - ((2 * 7) * 4)) = ((6 + -2) - ((2 * 7) * 4)) = ((6 + -2) - (14 * 4)) = (4 - (14 * 4)) = (4 - 56) = -48 = -48 = -48 = -48
(6 + (7 - 9)) = (6 + -1) = 5 = 4 = 4 = 4 (6 + -1) = 5 = 5 (6 + -1) = 5 (6 + 1) = 7 7 7 7 7 7 7
-4
-88
84
(((2 + 7) * 2) + 5) =
((9 * 2) + 5) = (18 + 5) = 23 = 38 = 38 = 38 (18 + 5) = 23 = 38 = 38 = 38 (18 + 5) = 29 = 43 = 53 (18 + 5) = 29 = 43 (29 + 43) = 44 Hayward (53)
(9 * 2) = 12 (18) = 36. (6 + 5) = 11 = 19 (6 + 11) = 20 (6 + 11) = 23 (6 + 11) = 23 (7 + 23) = 28 (7 + 23) = 28 (7 +
0
-20
20
(((9 + 6) - 6) * 2) =
(15 - 6) = 9. 9 (15 + 6) = 29.1 (19 + 9) = 32 43 (16 + 9) = 25 35 (16 - 16) = 0 0 ((16 - 16) + 8) AL² 8 (16 + 8) 24 (
(15 - 6) = 9. 3 (5 - 3) + 2 (2 + 2) = 4 2 ((2 - 2) + 2) = 2 2 ((1 - 2) + 2) = 2 -1 (2 + 2) = 6 8 9 8 2 2
-22
-36
14
(((5 + 2) * 1) + (4 - 5)) =
((7 * 1) + (4 - 5)) = (7 + (4 - 5)) = (7 + -1) = 6 = 5 = 5 = 5 (6 + -5) = 1 = 1 = 5 = 5 (6 + 1) = 7 = 7 = 7 1 (6 - 1) = 7
((7 * 1) + (4 - 5)) = * (7 + (4 - 5)) = (7 + -1) = 6 = 6 (7 + -1) = 6 (7 + 6) = 6 (7 + 6) = 7 (7 + 6) = 7 13 (7 + 6) =
-7
-8
1
(((7 + 2) * (8 - 3)) - ((1 * 5) + 9)) =
((7 * (8 - 3)) - ((1 * 5) + 9)) = ((7 * 5) + ((1 * 5) + 9)) = ((7 * 5) + (5 + 9)) = (35 + (5 + 9)) = (35 + 14) = 49 = 59 = 491 = 549 = 491 =
(9 * (8 - 3)) - ((1 * 5) + 9) = (9 * 5) = 45 = 453 (9 * 5) = 453 (9 * 5) = 453 (9 * 5) = 453 (45 - 45) = 0 0 (9 * 5) = 45
-11
-62
51
(((5 * 7) * (9 - 6)) * (2 + 7)) =
(35 * (9 - 6)) = (35 * 3) = 105 = 315 = 315 = 315 = 315 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3015 = 3
((35 * (9 - 6)) * (2 + 7)) = (35 * 3) = 1073 = 1073 ((35 * 3) + (2 + 7)) = (35 * 3) = 1073 = 1073 ((35 * 3) + (2 + 7)) = (35 * 3) = 1073 = 1073
-46
-50
4
(((6 - 6) + (9 + 6)) - 1) =
((0 + (9 + 6)) - 1) = ((0 + 15) - 1) = (15 - 1) = 14 = 15 = 14 = 14 = 14 = 14 = 14 = 14 (15 - 1) = 14 = 14 = 14 = 14 = 14 (15 - 4) = 14 = 14 = 14 = 14
(0 + (9 + 6)) = (0 + 15) = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15 = 15
0
-19
19
(((3 * 5) * 1) - 9) =
((15 * 1) - 9) = (15 - 9) = 6 = 3 = 3 = 3 = 3 = 3) = (30 - 6) = 24 = 24) = 24 = 24) = 24) = 24) = 24) = 24) = 24) = 24) = 24) = 24) = 24) = 24)
(15 * 1) = 15 = 15 (15) = 15 (15) = 15 (15) = 15 (15) = 15 (15) = 15 (15) = 15 (15) = 15 0 (15) = 15 0 (15) = 15 0 (15)
0
-18
18
(((2 - 2) + (6 + 2)) + 7) =
(0 + (6 + 2)) = (0 + 8) = 8 = 8 = 8 = 8 = 8 = 8 = 8 = 8 (0 + 8) = (8 = 8) = 8 = 8 = 8 (8 = 8) = 4 = 8 = 8 (8 = 8) = 4 = 8
(0 + (6 + 2)) = (0 + 8) = 0 = 0 = 0 = 0 = 0 = 0 (0 + 8) = 0 = 0 = 0 = 0 8 0 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-20
-21
1
(((4 - 1) * 3) * 8) =
((3 * 3) * 8) = (9 * 8) = 192 = 192. 72 (72 * 8) = 176 128 (72 + 176) = 248 344 (72 + 176) = 284 424 (72 * 8) = 176 448 ((72 + 176) = 284) 368
(=1 * 3) * 8) = (3 * 8) * 8) = 24 = 24 (3 * 8) * 8 = 24 = 24 (24) * 8 = 32 8 (24) * 8 = 32 32 ((8 * 8) * 8) = 32 96 (24) * 8 =
-2
-30
28
(((2 + 9) - 8) - 7) =
(11 - 8) = (3 - 7) = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4) = (4 - 4) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 =
(11 - 8) = 3? = 3 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2) = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2) = 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2)
-6
-16
10
(((7 * 3) * (5 + 7)) - 6) =
(21 * (5 + 7)) - 6 = (21 * 12) = 252 = 362 = 42 (21 * 12) = 144 = 192 = 294 (144 = 144) = 144 (144) = 144 (144) = 144 (144) = 144 (144) = 144 (144) = 144
(21 * (5 + 7)) = (21 * 12) = 252 = 288 = 144 = 96 = 96 = 144 = 96 Model 5 - (6 - 6) = (6 - 6) = 0 = 0 = 0 0 = 0 = 0 0 = 0 0 = 0
-17
-20
3
(((5 + 8) + (4 - 7)) + 1) =
((13 + (4 - 7)) + 1) = ((13 + -3) + 1) = (10 + 1) = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11
((13 + (4 - 7)) + 1) = ((13 + -3) + 1) = ((13 + -3) + 1) = (10 + 1) = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 = 11 =
0
-14
14
(((9 + 7) * 3) * (6 * (1 * 7))) =
((16 * 3) * (6 * (1 * 7))) = (16 * 3) * (6 * (1 * 7)) = (16 * 3) * (6 * 7) = 48 = 96 = 96 = 96 = 96 = 96 9 = 96 * (96) = 96 = 96 9 = 96 * 8 =
(16 * 3) (48)/9 (16 * 3) 8 (16 * 3) 48 (16 * 3) 48 (16 * 3) 48 (16 * 3) 48 (16 * 3) 48 (16 * 3) 48 (16 * 3) 48
-24
-114
90
(((1 + 1) - (7 - 7)) * 7) =
((2 - (7 - 7)) * 7) = ((2 - 0) * 7) = (2 * 7) = 14 = 28 = 46 = 46 = 46 (2 * 7) = 14 = 28 = 28 (2 * 7) = 28 = 28 4 (2 * 7) = 28 = 47 10 (
(2 - (7 - 7)) = (2 - 0) = 2 = 2 (*6 - (7 - 7)) = (2 - 0) = 2 = 2 ((2 - 0) = 2) = 2 (2 - 2) = 0 (2 - 2) = 0 0 (2 + 0) = 0
0
-33
33
(((8 + 2) * (9 * 5)) * 2) =
(10 * (9 * 5)) = (10 * 45) = 75 = 75 = 75 = 75 (75 - 75) = 0 = 0 (0 = 0) = 0 0 (0) = 0 0 0 (0) = 0 0 0 0 0 0 0 0 0
(10 * (9 * 5)) = (10 * 45) = 50 = 50 Visible in Informatics + Par (5) = 50 = 50
-23
-29
6
(((8 + 6) + (9 + 7)) - ((3 * 1) * (2 - 1))) =
((14 + (9 + 7)) - ((3 * 1) * (2 - 1))) = ((14 + 22) - ((3 * 1) * (2 - 1))) = ((14 + 22) - (3 * (2 - 1))) = (22 - (3 * 1)) = (22 - 3) = 21
(14 + (9 + 7)) = (14 + 16) = 30 = 36 = 36 = 36 (28 - 36) = -8 = -8 = -8 (28 - 36) = -8 (8 + 8) = 16 16 8 8 8 16
-31
-114
83
(((1 * 5) - 5) + 9) =
((5 - 5) + 9) = (0 + 9) = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 = 9 (0 + 9) = 9 = 9 =
(5 - 9) = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4 = -4) = (5 - 9) = -4 = -4 = -4 = -4 =
0
-15
15
(((4 * 4) * 1) - (1 + (9 + 2))) =
(16 * 1) = 16 A group of 1 is 16 = 16 = 16 = 16
(16 * 1) = 16 0 (16 + 11) = 33 47 (16 + 11) = 39 55 (16) + 4 20 (16) + 4 24 (16) + 4 24 (16) + 4 24 (16) + 4 28 8 (
-52
-87
35
(((6 * 2) * 6) * ((7 * 8) * 1)) =
(12 * 6) * ((7 * 8) * 1)) = (12 * 6) * ((7 * 8) * 1)) = (12 * 6) * (32 * 1)) = (12 * 6) * (32 * 1)) = (12 * 6) * (32 * 1)) = (12 * 6) * 32
(12 * 6) = 72 = 72 = 72 = 72 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
-49
-79
30
(((7 - 1) - (5 + 7)) + 9) =
((6 - (5 + 7)) + 9) = ((6 - 12) + 9) = (-6 + 9) = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 =
(6 - (5 + 7)) = (6 - 12) = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6
0
-20
20
(((2 * 5) - (6 - 4)) - ((4 - 1) + 9)) =
(10 - (6 - 4)) = (10 - 2) = 8 (10 - 2) = 8 (10 - 2) = 8 (8) = 8 (8) = 8 (8) = 8 8 (8) = 8 16 (8) = 8 16 (8) = 8
(10 - (6 - 4)) = (10 - 2) = 8 (8) = 12 = 12 = 12 = 12, also 3 = 6) = (12 + 12) = 24 (24 = 24) = 24 = 24 (12 - 24) = -12 (24) = -12 = -12 = 24 (
-71
-79
8
(((2 * 3) * (2 - 3)) * 8) =
((6 * (2 - 3)) * 8) = ((6 * -1) * 8) = ((6 * -1) * 8) = (6 * 8) = 48 = 48, 72, 96, 132 (48 * 8) = 96 = 96, 72, 72 (48 * 8) = 96 32 (48
(6 * (2 - 3)) = (6 * -1) = -6 = -6 = -6 = -6 = -6 (6 * -1) = -6 = -6 = -6 Now (6 = -6) = -6 = -6 0 = -6 = -6 0 = -6
-14
-22
8
(((7 + 4) - (8 - 3)) - ((8 - 1) * 8)) =
((11 - (8 - 3)) - ((8 - 1) * 8)) = ((11 - 5) - ((8 - 1) * 8)) = ((11 - 5) - (7 * 8)) = ((11 - 5) - 56) = (6 - 56) = -50 = -50 = -50 = -50 = -50
(11 - (8 - 3)) = (11 - 5) = 6 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7
-8
-82
74
(((2 * 1) - (2 - 2)) * ((5 - 8) - 5)) =
((2 - (2 - 2)) * ((5 - 8) - 5)) = ((2 - 0) * ((5 - 8) - 5)) = ((2 - 0) * (3 - 5)) = (2 * (3 - 5)) = (2 * -2) = -4 = -4 1 1
(2 - (2 - 2)) * ((5 - 8) - 5)) = (2 - (2 - 2)) * ((5 - 8) - 5) = (2 - 0) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0
-7
-49
42
(((4 - 7) - (1 * 2)) * (7 + (3 * 3))) =
((-3 - (1 * 2)) * (7 + (3 * 3))) = ((-3 - 2) * (7 + (3 * 3))) = ((-3 - 2) * (7 + 9)) = ((-3 - 2) * 14) = (-5 * 14) = -70 = -70 = 0 = 70
((? - (1 * 2)) * (7 + (3 * 3))) = (((4 - 7) * (7 + (3 * 3))) = ((4 - 7) * (7 + 9)) = ((4 - 7) * 16) = (-3 * 16) = -48 = -48 = -48 = -48 (
-11
-21
10
(((8 - 2) + (9 * 1)) - ((8 + 8) + 5)) =
(6 + (9 * 1)) - ((8 + 9) + 5)) = (6 + 9) = 15 = 24 = 24 = 24 (24 + 9) = 33 = 39 = 36 (24 + 9) = 45 = 54 (36 + 49) = 95 (55 - 49) = 6 14 (6
(6 + (9 * 1)) = (6 + 9) = 15 = 21 = 21 = 21 (15 + 9) = 24 = 33 = 63 (36 + 39) = 79 (39 + 33) = 96 (39 - 43) = 4 (4 - 4) = 0 0 (6 - 4)
-73
-87
14
(((6 * 6) - 1) + 6) =
(36 - 1) = 35 = 35 = 35 = 35 = 35 = 35 = 35 = 35 = 35 = 35 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5) = ((36 - 1) + 6) = (33 + 6) = 43 = 53 (33 + 6) = 39. No credit (
(24 - 1) = 23. 23 (24 - 1) = 23. 23 (24 + 1) = 25.9 27 ((24 + 1) + 6) = (24 + 6) = 30 30 (24 + 6) = 30 42 (18 - 6) = 12 6 ((
-14
-26
12
(((8 - 8) - 6) - 6) =
((0 - 6) - 6) = (-6 - 6) = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -12) = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -12 = -12) =
(0 - 6) = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6 = - 6) = (0 - 6) = -6 = -6 = -6 = -6 = -6 = -6 = -6 = -6) =
0
-16
16
(((9 + 8) - (1 + 1)) - (5 * (5 + 7))) =
((19 - (1 + 1)) - (5 * (5 + 7))) = ((19 - 2) - (5 * (5 + 7))) = ((19 - 2) - (5 * 12)) = (17 - (5 * 12)) = (17 - 120) = -99 = -99 = -99 = -99
((17 - (1 + 1)) - (5 * (5 + 7))) = ((17 - 2) - (5 * (5 + 7))) = (18 - (5 * (5 + 7)) - (5 * 12)) = (18 - (5 * 12)) = (18 - 60) = -42 = -42 = -
-11
-18
7
(((7 + 1) + (4 * 7)) + (9 - 5)) =
((8 + (4 * 7)) + (9 - 5)) = ((8 + 28) + (9 - 5)) = ((8 + 28) + 4) = (36 + 4) = 40 = 44 = 44 = 44 = 44 (36 + 4) = 44 = 44 = 44 However, 44 = 44
(8 + (4 * 7)) = (8 + 28) = 36 = 44 = 44 = 44 (34 + 44) = 66 = 110 = 154 (34 + 110) = 154 (74 + 154) = 225 (74 + 154) = 322 (74 + 274) = 381 (74 + 154) =
0
-46
46
(((6 - 1) - (4 - 3)) - ((3 * 1) + 5)) =
(5 - (4 - 3)) = (5 - 1) = (4 - 1) = 3 = 2 = 2 = 2 = 2 = 2 = 2 (4 - 1) = 3 = 3 = 3 = 2 (4 - 1) = 3 = 3 = 3 = 2 = 2 = 2 (4 - 1
(5 - (4 - 3)) = (5 - 1) = 4 (5 - 1) = 4 (5 - 1) = 4 (5 - 4) = 1 (1 + 4) = 5 5 ((1 - 4) + 1) = -3 -3 (1 - 1) = 1
-72
-79
7
(((4 - 2) * (2 - 9)) * (5 - (6 + 6))) =
((2 * (2 - 9)) * (5 - (6 + 6))) = ((2 * -7) * (5 - (6 + 6))) = ((2 * -7) * (5 - 12)) = (-14 * (5 - 12)) = (-14 * -7) = -98 = -98 = -98 = -98
((2 * (2 - 9)) * (5 - (6 + 6))) = ((2 * -7) * (5 - (6 + 6))) = ((2 * -7) * (5 - 15)) = (-14 * (5 - 15)) = (-14 * -10) = -56 = -56 = -
-1
-7
6
(((8 * 9) + (9 * 6)) + 4) =
((72 + (9 * 6)) + 4) = ((72 + 54) + 4) = (126 + 4) = 134 (126 = 134) = 134 (126) + 4 (126) + 4 (126) = 134 10 (126) + 4 (126) + 4 10 (126
(72 + (9 * 6)) = (72 + 54) = 96 = 126 = 196 = 196 (72 + 56) = 236 = 346 = 430 (72 + 236) = 112 = 344 (112 = 344) = 352 (112 = 352) = 352 (352 352 352
-5
-22
17
(((5 * 6) * (8 + 1)) * (3 + 1)) =
((30 * (8 + 1)) * (3 + 1)) = ((30 * 9) * (3 + 1)) = ((30 * 9) * 4) = (270 * 4) = 654 = 134 = 134 (54 + 4) = 60 = 64 (54 + 4) = 60 (54 - 54)
(30 * (8 + 1)) = (30 * 9) = 270 = 270 = 270 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = 30 = (3 + 30) = (3) = 33 = 30 = 30 = 30 = 30 = 30 = 30 = 30 =
-4
-46
42
(((4 * 3) - (2 - 1)) - 8) =
((12 - (2 - 1)) - 8) = (9 - (2 - 1)) = (9 - 1) = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 = 7 =
(12 - (2 - 1)) = (12 - 1) = 11 = 11 = 11 = 11 = 11 = 11 (9 + 11) = 22 = 29 (22 - 11) = 11 (9) = 13 (13) = 11 (13) = 11 (11) = 11 (11) = 11
-11
-20
9
(((2 - 4) + 6) - 5) =
((-2 + 6) - 5) = (4 - 5) = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1) = (4 - 1) = -1 =
(2 + 6) = 8 = 10 = 10 = 10 = 10 = 10 = 10 = 10 (2 + 6) = 14 = 16 = 16 2 ((2 + 6) - 15) = (8 - 15) = -7 = -7 -3 (2 - 15) = -13 = -13 -1
0
-18
18
(((9 + 5) * 3) * ((7 * 4) - (2 + 9))) =
((14 * 3) * ((7 * 4) - (2 + 9))) = (28 * ((7 * 4) - (2 + 9))) = (28 * (14 - (2 + 9))) = (28 * (14 - 11)) = (28 * 3) = 96 = 231 = 69 = 72 = 72 (72) =
(14 * 3) = 38 = 126 = 186 = 186 = 186 = 186 (14 * 3) = 34 = 66 = 102 (14 * 3) = 34 = 34 (14 * 3) = 34 (14 * 3) = 34 34 (14 * 3) = 34 42 (14 * 3) =
-31
-95
64
(((7 - 3) * (3 + 8)) - ((8 + 3) * 5)) =
(2 * (3 + 8)) - ((8 + 3) * 5)) = (2 * 11) - (22 * 5)) = (2 * 11) - 50 = -50 = -50 = -50 = -50 = -50 (2 * 11) - (50 + 50) = 45 = 90 ((2 *
((4 * (3 + 8)) - ((8 + 3) * 5)) = (4 * (9 + 8) * 5) = (4 * 17) = 68 = 68 Which is the second smallest value? 3 0.3 0.3 0.3 0.3
-45
-60
15
(((4 + 1) * 7) * (2 * (8 + 2))) =
((5 * 7) * (2 * (8 + 2))) = ((5 * 7) * (2 * 10)) = (35 * (2 * 10)) = (35 * 20) = 700 = 1070 = 1070 = 1070 = 1070 (700 * 20) = 1300 = 1070 = 1070 (700
((5 * 7) * (2 * (8 + 2))) = (35 * (2 * (8 + 2)) * (2 * 10)) = (35 * 14) = 490 = 590 = 90 = 90 (4*o) = 8 + 8 = 16 (4 * 8) = 16 (4 * 8)
0
-30
30
(((2 + 3) - 6) + 5) =
((5 - 6) + 5) = (-1 + 5) = 4 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 =
(5 - 5) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0) = 0 = 0 = 0 = 0 = 0 = 0 = 0) = 0 = 0 = 0 = 0 = 0 = 0 =
0
-15
15
(((8 + 5) + 6) * 5) =
(13 + 6) = 19 = 29 = 19 = 19 = 19 (19 + 19) = 34 = 29 = 19 (24 + 19) = 44 = 59 (24 + 19) = 35 (34 + 59) = 75 (34 + 59) = 95 (34 - 59) = -37 (29 -
(13 + 6) = 19 = 29. (9) + 25 (13 + 4) = 17 (17) + 19 (18) + 19 (18) = 19 (18) = 19 (18) = 19 (18) = 19 (18) = 19 (18) = 19 (
-14
-29
15
(((6 + 4) + (7 + 8)) * 3) =
((10 + (7 + 8)) * 3) = ((10 + 15) * 3) = (25 * 3) = 75 (25 * 3) = 75 75 75 75 75 75 75 75 75 75 75 75 75
(10 + (7 + 8)) = (10 + 21) = 41 = 41 (21 - 41) = -20 = -19 -1 (21 - 21) = -2 (1 - 2) (1 - 2) (1 - 2) (1 - 2) -1 (1 -
-8
-33
25
(((9 * 1) * 6) * ((4 + 1) * 2)) =
(9 * 6) * ((4 * 1) * 2)) = (9 * 6) * (4 * 2) = 18 * 2 = 36 = 42 = 72 = 72 (18 * 2) * (4 * 2) = 36 * 2 = 72 (18 * 2) * (4 * 2) = 72 * 2 =
(9 * 6) = 54 (9 * 6) = 54 (54 + 54) = 180 222 (54) = 42 78 (54) = 42 84 (54) = 42 117 (54) = 42 42 (54) = 42 93 (54) = 42 54
-26
-54
28
(((7 + 3) - (9 * 8)) * 1) =
((11 - (9 * 8)) * 1) = ((11 - 72) * 1) = (-61 * 1) = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61 = -61
(10 - (9 * 8)) = (10 - 72) = -62 = -62 = -62 = -62 = -62 = -62 = -62 = -62 = -62 = -62 = -62 = -62 = -2 = -62 = -62 = -62 = -62 = -
-5
-18
13
(((4 + 5) * 3) - ((4 * 3) * 4)) =
((9 * 3) - ((4 * 3) * 4)) = ((9 * 3) - (12 * 4)) = (27 - (12 * 4)) = (27 - 48) = -15 = -15 = -15 1 (27*v) = (27 - 6) = 21 = 21 2
((9 * 3) - ((4 * 3) * 4)) = (27 - ((4 * 3) * 4)) = (27 - 12) = 9 = 9 = 9 = 9 = 9 = 9 (27 - 11) = 15 = 8 = 9 = 9 (27 + 15) = 15 = 9 =
-4
-31
27
(((5 * 6) + (7 + 9)) + 4) =
(30 + (7 + 9)) = ((30 + 16) + 4) = (56 + 4) = 60 = 72 = 72 (56 + 4) = 60 = 62 (60 + 74) = 134 (74 - 74) = 0 0 = 0 0 What (44 - 79) = -25 -
(150 + (7 + 9)) = (150 + 16) = 206 = 206 = 206 = 206 Top 7 Implications 1) Daily @ (150) = (206) = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 206 = 202 = 202 = 202 =
-8
-23
15
(((9 * 3) + 7) - 6) =
(27 + 7) = 34 = 51 = 51 = 51 = 51 = 51 = 21 = 21 = 21 = 21 = 21 = 21 = 21 = 21 = 21 (27 - 6) = 21 = 15 for from 15 for from 15 for from 15 for from 15 (27 - 1) = 27 for from 15 for from 15 for from 15
(27 + 7) = 40. (41 + 30) = 73 (27 + 6) = 39 (39 + 69) = 126 (90 + 66) = 171 (21 - 69) = 42 (39 + 84) = 117 (69 + 87) = 192 (96) = 201 (81)
-14
-22
8
(((8 + 1) * (5 - 3)) + (1 - 7)) =
((9 * (5 - 3)) + (1 - 7)) = ((9 * 2) + (1 - 7)) = ((9 * 2) + -6) = (18 + -6) = 12 = 6 = 6 = 6 = 6 = 6 = 6 = 6 = 6 = 6 (6 + 6) = 18 =
(9 * (5 - 3)) = (9 * 2) = 18 = 36 = 36 = 36 = 36 (18 + 36) = 54 = 78 + 54 (18 + 54) = 72 = 84 (74 + 72) = 132 (78 + 74) = 170 (78 + 74) = 174 (74
0
-48
48
(((4 + 6) * 6) + 9) =
(10 * 9) = 90 (10 * 9) = 90 0 (10 * 9) = 90 90 (10 * 9) = 90 90 Here is (10 * 9) = 90 90 (10 * 9) = 90 90 6 6 6 6 6 6 6
(10 * 6) = 60 50 (10 * 6) = 60 30 (50 + 60) = 10 110 (50 + 60) = 10 160 ((50 + 60) + 9) = (850 + 9) = 997 KP = 987 KP = 987 KP =
-20
-25
5
(((5 + 4) - (8 + 3)) + (1 + (2 - 6))) =
((9 - (8 + 3)) + (1 + (2 - 6))) = ( (9 - 11) + (1 + (2 - 6))) = ((9 - 11) + (1 + -4)) = (2 + (1 + -4)) = (2 + -3) = -1 = -1 = -1 =
((9 - (8 + 3)) + (1 + (2 - 6))) = ((9 - 11) + (1 + (2 - 6))) = ((9 - 11) + (1 + -4)) = ((9 - 11) + -3) = (2 + -3) = -1 = -1 = -
-5
-10
5
(((8 * 1) + (8 - 7)) * ((9 - 4) * (1 - 2))) =
((8 + (8 - 7)) * ((9 - 4) * (1 - 2))) = ((8 + 1) * ((9 - 4) * (1 - 2))) = ((8 + 1) * (5 * (1 - 2))) = ((8 + 1) * (5 * -1)) = (9 * (5 *
(8 + (8 - 7)) * ((9 - 4) * ((9 - 4) * (1 - 2))) = (8 + (8 - 7)) * ((9 - 4) * (1 * (1 - 2))) = (8 + (8 - 7)) * ((9 - 4) * (1 * -1))
-19
-89
70
(((3 * 1) - (2 - 8)) + (4 - (7 * 9))) =
((3 - (2 - 8)) + (4 - (7 * 9))) = ((3 - 6) + (4 - (7 * 9))) = ((3 - 6) + (4 - 63)) = ((3 - 6) + -59) = (-3 + -59) = -62 = -62 (62 + -
imates (1 - (2 - 8)) = irez (1 - -6) = (7 - -7) = 14 = 23 = 29 (4 + -14) = -10 = -10
-24
-86
62
(((7 * 7) * (3 * 7)) + ((8 * 7) * (3 - 9))) =
((49 * (3 * 7)) + ((8 * 7) * (3 - 9))) = (((49 * 21) + ((8 * 7) * (3 - 9))) = (49 * (69 + (6 - 9)) + ((8 * 7) * (3 - 9))) = (49 * (69 + -3)
(49 * (3 * 7)) = (49 * 21) = 201 = 341 = 41 (49 * 21) = 201 = 91 = 130 (49 * 21) = 201 = 91 (49 * 21) = 201 In other words 323 = 91 31 17 In other words 323
-68
-122
54
(((2 * 9) + (4 + 7)) - (7 - 3)) =
((18 + (4 + 7)) - (7 - 3)) = ((18 + 11) - (7 - 3)) = ((18 + 11) - 4) = (29 - 4) = 25 = 21 (25 - 4) = 21 (21 + 21) = 36 (21 - 21) = 0 0 (21
(18 + (4 + 7)) = (18 + 13) = 31 = 52 = 52 (18 + 13) = 59 = 61 (18 + 13) = 59 = 59 (18 + 13) = 59 (27 + 17) = 86 (27 + 17) = 86 (27 +
0
-55
55
(((3 + 7) + 1) * ((4 * 2) * (7 + 2))) =
((10 + 1) * ((4 * 2) * (7 + 2))) = ((10 + 1) * (8 * (7 + 2))) = (11 * (8 * 9)) = (11 * 72) = 72 = 72 = 72 = 72 (72 = 72) = 72 = 72 Then to an
~~(10 * ((4 * 2) * (7 + 2)))~~ = ~~(10 * 8)~~(10 * 8) = 80~~(10 * 8) = 80~~(10 * 8) = 80*(10 * 8) = 80*(10 * 8) = 80*(10 * 8) = 80*p
-21
-61
40
(((3 + 2) * (7 * 1)) * 2) =
((5 * (7 * 1)) * 2) = ((5 * 7) * 2) = (35 * 2) = 70 = 70cut = 70 = 10 = 70 = 70 = 70 = 70 = 70 = 70 = 70 = 70 = 70 = 70 = 70 = 70 = 70
(5 * (7 * 1)) = (5 * 7) = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5) = (5 * 7) = 5 = 5 = 5 = 5 = 5 = 5 = 5) = 5 = 5 = 5 =
0
-21
21
(((2 - 6) * (7 + 9)) + 1) =
((2 * (7 + 9)) + 1) = ((2 * 18) + 1) = (36 + 1) = 37 = 37. 37 (36 + 1) = 37. 1 = 37. 1 38 (36 - 1) = 37. 1 37 (36 + 1) = 37. 1 38
(4 * (7 + 9)) + 1 = (4 * 20) = 80 = 80 = 80 = 80 (4 * 20) = 80 = 80 20 = 80 80 80 400 160 80 80 80 80 80 80 80
-21
-27
6
(((9 + 4) * (4 + 9)) + ((2 - 7) - (7 + 3))) =
((13 * (4 + 9)) + ((2 - 7) - (7 + 3))) = ((13 * 13) + ((2 - 7) - (7 + 3))) = ((13 * 13) + (-5 - (7 + 3))) = ((13 * 13) + (-5 - 10)) = (121 + (-5
((15 * (4 + 9)) + ((2 - 7) - (7 + 3))) = ((15 * 13) + ((2 - 7) - (7 + 3))) = ((15 * 13) + (-5 - (7 + 3))) = (135 + (-5 - (7 + 3))) = (135 + (
-23
-40
17
(((8 * 3) * 4) * ((1 - 5) - 8)) =
(24 * 4) = 96 = 96 (24 * 4) = 96 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(24 * 4) = 96 = 96 (24 * 4) = 96 96 8 88 96 48 48 48 48 48 48 48 48 48 48 48 48 48 48
-76
-92
16
(((1 * 3) - 4) * 7) =
((3 - 4) * 7) = (-1 * 7) = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7 = -7) = (7 = -7) = -7 = -7 = -7 = -7 = -7 = -7 = -7 =
(3 - 4) = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1 = -1) = (1 - 1) = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0
0
-14
14
(((2 + 4) - (5 + 7)) + ((8 - 3) - (8 + 7))) =
((6 - (5 + 7)) + ((8 - 3) - (8 + 7))) = (((6 - 12) + ((8 - 3) - (8 + 7))) = ((6 - 12) + (5 - (8 + 7))) = ((6 - 12) + (5 - 15)) = (6 + (5 -
((6 - (5 + 7)) + ((8 - 3) - (8 + 7))) = ((6 - 12) + ((8 - 3) - (8 + 7))) = ((6 - 12) + (11 - (8 + 7))) = ((6 - 10) + (11 - 15)) = (4 +
-23
-33
10
(((5 + 6) + 9) + ((9 - 4) - 9)) =
((11 + 9) + ((9 - 4) - 9)) = (20 + ((9 - 4) - 9)) = (20 + (5 - 9)) = (20 + -4) = 16 = 16 = 16 = 16 = 16 (16 - 16) = 0 = 16 = 16 0 = 16 = 16
(11 + 9) = 22. 7 ((5 + 9) + ((9 - 4) - 9)) = (11 + 9) = 22. 17 (11 + 9) = 22. 29 (11 - 11) = 2 1 (1 + 3) = 4 4 (-2 - 1) =
-9
-58
49
(((8 * 7) + (6 * 4)) * 1) =
((56 + (6 * 4)) * 1) = ((56 + 24) * 1) = (80 * 1) = 80 = 80 = 80 = 80 = 80 ((80 = 80) * 1) = 80 = 80 (80 * 1) = 80 (80 = 80) = 80 (80 = 80) = 80
(56 + (6 * 4)) = (56 + 24) = 80 = 96 = 96 = 96 (56 + 24) = 116 = 160 = 160 (16 + 96) = 128 = 128 (128 + 128) = 256 (128 + 128) = 256 (256 = 256) (256 - 256) =
0
-20
20
(((6 * 7) - (1 - 8)) + (8 * 6)) =
(42 - (1 - 8)) + (8 * 6) = (42 - -7) = 491. 5 (42 - -6) = 48. 54 ((8 - 8) - (8 * 6)) = (8 - (8 * 6)) = (8 - 48) = -40 = -40 -
(42 - (1 - 8)) = (42 - -7) = 49 = 56 = 50 (42 - 7) = 49 = 49 (42 - 7) = 53 (42 - 7) = 49 (42 - 7) = 49 (42 - 7) = 49 31 ((((6 * 1) - 3
-56
-57
1
(((9 * 8) - (3 * 7)) * (1 * (1 - 9))) =
((72 - (3 * 7)) * (1 * (1 - 9))) = ((72 -21) * (1 * (1 - 9))) = ((72 - 21) * (1 * -8)) = (63 * (1 * -8)) = (63 * -8) = -84 = -84 = -84 =84
((48 - (3 * 7)) * (1 * (1 - 9))) = ((48 - 21) * (1 * (1 - 9))) = ((48 - 21) * (1 * -8)) = (21 * (1 * -8)) = (21 * -8) = -84 = -84 = -84 = -84
-11
-14
3
(((3 + 3) - (1 + 8)) - 5) =
((6 - (1 + 8)) - 5) = ((6 - 9) - 5) = (-3 - 5) = -8 = -8 = -8 = -8 = -8 = -8 = - (8 - 8) = 0 = 0 = 0 (0 = 0) = 0 (0 = 0) =
(6 - (1 + 8)) = (6 - 9) = -3 = -3 = -3 = -3 = -3 = -3 = -3 = -3 = -3 = -3 = -3 = -3 (6 - (1 + 8)) = (6 - 9) = -3 = -3 = -
0
-20
20
(((2 - 3) + 9) * ((3 - 4) * (9 + 8))) =
((-1 + 9) * ((3 - 4) * (9 + 8))) = ((-1 + 9) * (1 * (9 + 8))) = ((-1 + 9) * (1 * 17)) = (8 * (1 * 17)) = (8 * 17) = 71 = 73 = 73 = 73 (7 *
((-1 + 9) * ((3 - 4) * (9 + 8))) = ((-1 + 9) * (1 * (9 + 8))) = (8 * (1 * 17)) = (8 * 31) = 88 = 176 = 256 = 260 = 260 = 260 = 260 = 260 = 260 = 260 (
-10
-31
21
(((7 + 8) - 6) * 2) =
(15 - 6) = 9 = 5 = 4 = 4 = 4 (9 - 9) = 0
(15 - 6) = 9 + 3. 6 (1 + 9) = (10) = 9 + 3. 9 (2 + 9) = 13 = 17 25 (2 + 9) = 11 = 13 17 (2 + 9) = 11 = 11 13 (2 + 9) = 9
-14
-18
4
(((8 * 4) * (6 - 1)) - (7 * 7)) =
((32 * (6 - 1)) - (7 * 7)) = ((32 * 5) - (7 * 7)) = (32 - 7) = 25 = 9 = 9 (32 - 7) = 23 (32 - 7) = 21 (28) = 17 (32)*( 17 ) = 17 (
(32 * (6 - 1)) = {32 * 5) - (7 * 7) = (320 - 7) = 307 = 307 = 307 = 307 = 307 = 307 = 307 = 307 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207 = 207
-21
-35
14