Add contest day metadata and official source

README.md

@@ -15,6 +15,8 @@ dataset_info:
   features:
   - name: id
     dtype: int64
+  - name: day
+    dtype: int64
   - name: problem
     dtype: string
   splits:
@@ -25,13 +27,18 @@ dataset_info:
 # IMO 2026 Problems
 
 The six IMO 2026 problem statements, indexed from `0` through `5` in contest order.
+IDs `0`–`2` are from Day 1, and IDs `3`–`5` are from Day 2.
 
 ## Schema
 
 - `id`: zero-based problem identifier (`0` corresponds to Problem 1).
+- `day`: contest day (`1` or `2`).
 - `problem`: complete English problem statement.
 
 ## Source
 
 Extracted from the problem statements in SignalPilot Labs' AutoFyn IMO 2026 results:
 https://github.com/SignalPilot-Labs/AutoFyn/tree/production/results/imo-2026
+
+Official IMO 2026 edition page:
+https://www.imo-official.org/editions/2026/

data/train.jsonl

@@ -1,6 +1,6 @@
-{"id":0,"problem":"There are 2026 integers greater than 1 written on a blackboard, not necessarily distinct. In one move, Confucius chooses two integers m > 1 and n > 1 written in different positions and replaces them by gcd(m,n) and lcm(m,n)/gcd(m,n). He continues making moves for as long as a move is possible. (a) Prove that, regardless of his choices, the process terminates after finitely many moves with exactly one integer M > 1 on the board. (b) Prove that the value of M is independent of all choices made during the process."}
-{"id":1,"problem":"Let ABC be a triangle, and let M and N be the midpoints of AB and AC, respectively. Let K and L be chosen inside triangles BMC and BNC, respectively, such that K lies inside angle LBA, L lies inside angle ACK, and angle KBA = angle ACL, angle LBK = angle LNC, and angle LCK = angle BMK. If O is the circumcentre of triangle AKL, prove that OM = ON."}
-{"id":2,"problem":"Let n be a positive integer. Liu Bang and Xiang Yu have a stick of length 1. First Liu Bang marks at most n points on the stick, and then Xiang Yu marks at most n further points; all marked points are distinct. The stick is cut at every marked point. The players then alternately claim unclaimed pieces, with Liu Bang moving first, and each player seeks to maximize the total length of the pieces he claims. Determine the largest number c that Liu Bang can guarantee, regardless of Xiang Yu's play."}
-{"id":3,"problem":"Shan-Yu and Mulan are playing a game. Let theta be an angle with 0 degrees < theta < 180 degrees known to both players. Initially, Shan-Yu makes a paper triangle T with measurements of his choice. Then they repeatedly perform the following steps: If T has at least one angle measuring exactly theta, then the game stops and Mulan wins. Otherwise, Mulan chooses a point P on the perimeter of T, different from its three vertices. She then makes a straight cut from P to the opposite vertex of T, splitting it into two triangles. Shan-Yu discards one of the two triangles. The remaining triangle becomes the new T. For which real values of theta can Mulan guarantee her victory in finitely many steps, no matter how Shan-Yu plays?"}
-{"id":4,"problem":"Determine all functions f: R_{>0} -> R_{>0} such that sqrt((x^2 + f(y)^2)/2) >= (f(x) + y)/2 >= sqrt(x f(y)) for every x,y in R_{>0}."}
-{"id":5,"problem":"Let a_1, a_2, a_3, ... be an infinite sequence of positive integers greater than 1. Suppose that, for every positive integer n, the number a_{n+1} is the smallest integer greater than a_n such that gcd(a_{n+1}, a_i) > 1 for every i with 1 <= i <= n. Prove that there exist positive integers T and L such that a_{n+T} = a_n + L for every positive integer n."}
+{"id":0,"day":1,"problem":"There are 2026 integers greater than 1 written on a blackboard, not necessarily distinct. In one move, Confucius chooses two integers m > 1 and n > 1 written in different positions and replaces them by gcd(m,n) and lcm(m,n)/gcd(m,n). He continues making moves for as long as a move is possible. (a) Prove that, regardless of his choices, the process terminates after finitely many moves with exactly one integer M > 1 on the board. (b) Prove that the value of M is independent of all choices made during the process."}
+{"id":1,"day":1,"problem":"Let ABC be a triangle, and let M and N be the midpoints of AB and AC, respectively. Let K and L be chosen inside triangles BMC and BNC, respectively, such that K lies inside angle LBA, L lies inside angle ACK, and angle KBA = angle ACL, angle LBK = angle LNC, and angle LCK = angle BMK. If O is the circumcentre of triangle AKL, prove that OM = ON."}
+{"id":2,"day":1,"problem":"Let n be a positive integer. Liu Bang and Xiang Yu have a stick of length 1. First Liu Bang marks at most n points on the stick, and then Xiang Yu marks at most n further points; all marked points are distinct. The stick is cut at every marked point. The players then alternately claim unclaimed pieces, with Liu Bang moving first, and each player seeks to maximize the total length of the pieces he claims. Determine the largest number c that Liu Bang can guarantee, regardless of Xiang Yu's play."}
+{"id":3,"day":2,"problem":"Shan-Yu and Mulan are playing a game. Let theta be an angle with 0 degrees < theta < 180 degrees known to both players. Initially, Shan-Yu makes a paper triangle T with measurements of his choice. Then they repeatedly perform the following steps: If T has at least one angle measuring exactly theta, then the game stops and Mulan wins. Otherwise, Mulan chooses a point P on the perimeter of T, different from its three vertices. She then makes a straight cut from P to the opposite vertex of T, splitting it into two triangles. Shan-Yu discards one of the two triangles. The remaining triangle becomes the new T. For which real values of theta can Mulan guarantee her victory in finitely many steps, no matter how Shan-Yu plays?"}
+{"id":4,"day":2,"problem":"Determine all functions f: R_{>0} -> R_{>0} such that sqrt((x^2 + f(y)^2)/2) >= (f(x) + y)/2 >= sqrt(x f(y)) for every x,y in R_{>0}."}
+{"id":5,"day":2,"problem":"Let a_1, a_2, a_3, ... be an infinite sequence of positive integers greater than 1. Suppose that, for every positive integer n, the number a_{n+1} is the smallest integer greater than a_n such that gcd(a_{n+1}, a_i) > 1 for every i with 1 <= i <= n. Prove that there exist positive integers T and L such that a_{n+T} = a_n + L for every positive integer n."}