MathDB

15

Part of 2005 Postal Coaching

Problems(1)

A set

Source: Indian Postal Coaching 2005

9/23/2005
Let XX be a set with ∣X∣=n|X| = n , and let X1,X2,...XnX_1 , X_2 ,... X_n be the nnsubsets eith ∣Xj∣≥2|X_j| \geq 2, for 1≤j≤n1 \leq j \leq n. Suppose for each 22 element subset YY of XX, there is a unique jj in the set 1,2,3....,n1,2,3....,n such that Y⊂XjY \subset X_j . Prove that Xj∩Xk≠ΦX_j \cap X_k \not= \Phi for all 1≤j<k≤n1 \leq j < k \leq n
algebra unsolvedalgebra