Balls in baskets

Question

There are 16 baskets: 4 red, 4 blue, 4 green and 4 black. Each basket contains a ball from one of the 4 colours (see image). You can pick up a ball from one basket and swap it with a ball from another basket. What is least number of swaps needed to make every basket contain a ball of the same colour as the basket?

combinatorics mathematics

Arale · Accepted Answer

If the baskets are named with the rows and columns:

A B C D
E F G H
I J K L
M N O P

I will first try and swap the baskets' containers where the two will be solved with just 1 swap:

Then finish the puzzle with the smallest number of swaps:

So the smallest number of swaps needed is

EDIT: <-> is a swap, e.g. A<->B is basically swapping whatever's in A to B.

Balls in baskets

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