Permutations

2 articles

Combinatorics & Discrete Math LycéeAnalyse10 min

Nine Digits, Four Windows, and a Middle That Cannot Move

Nine slots hold the digits 1 to 9 and four overlapping windows each add to 20. One subtraction pins the centre digit to 5 with no search at all, and the same structure classifies every arrangement: there are 96 of them, falling into 48 mirror pairs. Change the target and the centre is forced to an odd digit that sometimes admits nothing.

Combinatorics & Discrete Math LycéeExplication9 min

One in Three, and the Card That Was Never in the Problem

Wind appears nowhere in the winning condition, so delete it: three cards in six equally likely orders, and you win in the two where fire comes last. One in four is the correct probability that fire is last of all four cards, a strictly smaller event, and the gap is exactly one twelfth.