Physics, Chemistry, Maths Forum

Math's challenge

Math's challenge

by Gurpreet Singh -
Number of replies: 2

Q1: The 100 integers from 1 to 100 are each written onto 100 index cards, which are then thoroughly shuffled. To put the cards back into their natural ordering, the only operation allowed is for a pair of cards to be swapped. Is it always possible to put the 100 cards back in order using 74 or fewer of these swap operations?

In reply to Gurpreet Singh

Re: Math's challenge

by Srinath Murthy -

Best case: 1, 2, 3, 4, ..........., 99, 100 -> No swap required

A worst case: 2, 3, 4, 5, .................100, 1 -> 99 swaps required (between 100 & 1, then 99 & 1, then 98 &1 and so on)

The answer should be 99 not 74.