14 December 2019
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From New Scientist #3259, 14th December 2019 [link] [link]
Three short-sighted spiders are clustered at the vertex of a wire frame in the shape of a tetrahedron. The spiders know that there is an ant walking around the frame, but they have no idea where it is. They will only be able to spot it when they are practically on top of it. The ant, on the other hand, has excellent eyesight and can plan its route accordingly to avoid the spiders. Given that the ant walks slightly slower than the spiders, is there a way for the ant to escape the spiders indefinitely? Or can the spiders find a strategy to be certain of catching the ant?
From New Scientist #3237, 6th July 2019 [link] [link]
Betty works at a cash register in the US. When you purchase something from her, Betty always gives you your change the sensible way: by selecting the largest coins that don’t take her over the amount that she owes you. For example, if she owed you 37 cents, she would first pick out a quarter (25 cents), then a dime (10 cents) then two pennies (a cent each).
However, this morning she has run out of nickels (5 cents) to give out as change, though she has plenty of pennies, dimes and quarters. When she gives you your change, you notice that she has given you twice as many coins as she could have done if she hadn’t been so keen to always start with the largest coin. What is the smallest possible monetary value of the change she has given you?