Jose A. Gomez, Maria Luisa Perez-Segui, R. A. Sáenz, R. Valdez
2017.12.1Mathematics Magazine
tlooto Summary
Mathematicians prove that any partition of a standard deck into 13 sets can be transformed into another partition with each set having exactly 13 cards.
Abstract
2033. Proposed by Yoshihiro Tanaka, Hokkaido University, Sapporo, Japan. A deck is the collection of all 52 pairs (“cards”) of the form (n, s) where 1 ≤ n ≤ 13 is the number on the card, and the suit s of the card is one of the symbols ♦, ♥, ♠, ♣. Given an arbitrary partition of a deck into 13 sets S1, S2, . . . , S13 of 4 cards each, prove that there exists a corresponding partition C1, C2, C3, C4 of the deck into 4 sets of 13 cards each, such that each of the parts Ci (1 ≤ i ≤ 4) satisfies:
Citation format
GOMEZ, Jose A., et al. Problems. Mathematics Magazine, 2017, 90: 383–384.