Suppose we are given 5 pairs of balls in 5 colours, such that all the balls have the same weight.

Now we are told that someone has put two 1 gram diamonds in one of the 5 pairs of balls, so that now there is exactly one pair of balls having same colour, where the two balls each are 1 gram heavier than the other balls.

You are given a scale with two pans, marked as the 'left pan' and the 'right pan', and a digital display which shows the signed difference in the weights (in grams) between the 'left pan' and the 'right pan'.

So if we put 3 grams in the 'left pan' and 5 grams in the 'right pan' it will show -2 grams, and if we swap the weights it will show +2 grams.

You can put as many balls into each of the pan as you like.

What is the minimum number of weighings that you need to take in order to determine the colour of the balls containing the diamonds?

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