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Today Puzzle #619

Puzzle No. 619– Tuesday 26 November

To give the impression that their minds are occupied with high and abstract concepts, academic scientists wear odd socks on purpose. If I want to wear a unique combination (no repeats, no matched pairs) every day for a week, how many different colours of sock do I need?

Today's #PuzzleForToday has been set by Dr Andrew Brown, Lecturer in School of Maths, Queen’s University Belfast.

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With four colours (e.g red, green, blue and yellow) there are only six unique combinations: RG, RB, RY, BG, BY, GY. Thus to do 7 days I would need 5 colours. As a bonus, if I have 5 colours I have enough for 10 days: with 5 colours there are 5X5=25 total combinations. 5 of them are matched pairs, leaving 20. And swapping the order doesn’t matter: BG is the same as GB, so only half (20/2=10) give unique combinations.

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