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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?

enter image description here

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  • $\begingroup$ Don't you hate it when a puzzle requires so much longer to make (and draw!) than to solve? :( $\endgroup$ Commented May 5, 2021 at 5:47

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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:

A<->E, J<->K, F<->O, G<->P

Then finish the puzzle with the smallest number of swaps:

D<->L, D<->H, B<->D

So the smallest number of swaps needed is

7 swaps!

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

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  • $\begingroup$ That is correct! Well done and welcome to Puzzling. $\endgroup$ Commented May 1, 2021 at 12:28

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