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# Maths Week: Your Friday puzzle

Fancy another mathematics challenge? (And get the answer to yesterday’s puzzle.)

IT’S FRIDAY OF Maths Week… let us know in the comments how you’ve been doing with our puzzles.

Day seven – Sock it to me

Mathematicians have an unusual interest in socks. Far more than the general population. They also have the habit of not folding them into pairs and mixing them up in drawers in dark rooms. Some of them also like to keep their socks in black sacks.

30 black socks and 30 white socks are jumbled in a big black sack. They are identical apart from colour. You reach into the sack and take out several socks without first looking at them.

• How many would you have to take out to be certain of one black pair and one white pair?
• What is the smallest number of socks you would have to take out to be certain of having on matching pair.

Now suppose that the bag contains 15 white, 13 black and 11 blue socks.

• How many do you have to take out to be sure of a matching pair?
• How many do you have to take out to be certain of a white pair?
• Imagine that you have three sock drawers. One of them contains two white socks, another contains two black socks, and the third contains one white and one black sock. The drawers are labelled. One says All White, another says All Black, and the third says Mixed, but someone has switched the labels so that every drawer is incorrectly labelled. You are allowed to take just one sock out of just one of the drawers, only seeing that sock. The goal is to determine correctly the contents of all three boxes. What should you do?
• In a sock drawer, all are blue except two, all are green except two and all are white except two. How many socks are there?

1. She marks off three points dividing the rope into 5m, 12m, 13m lengths (a Pythagorean
triple). She stretches this out to a triangle with these marks at the corner. This will be a right angle triangle.

2. 8³+13³ 14³ cannot be true because 8x8x8 must be even; 13x13x13 must be odd and an even and an odd must be odd. Meanwhile 14x14x14 must be even.

3. This puzzle was featured by Martin Gardner in Scientific American, Jul 1971. Time reported (7 March 1938) that one Samuel Isaac Krieger claimed to have found a counterexample to Fermat’s unproved last theorem.

Krieger’s claim of 1,324ᴺ 731ᴺ=1,961ᴺ was poorly thought out and a reporter on the New York Times noticed that the first number, 1,324, raised to any power must end in 6 or 4 (as it has 4 at the end). The other two numbers, 731 and 1,961, raised to any power must still end in 1. Adding a number ending in 6 or 4, to a number ending in 1, cannot produce a number ending in 1. Therefore the claim was bogus.

Come back tomorrow at 7.30pm for the answers to today’s puzzle.

The puzzles this week have been compiled by Eoin Gill and Colm Mulcahy of Maths Week Ireland / South-East Technological University (SETU).

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The Journal Team