Enigma 1387: Something to declare
5 October 2013
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From New Scientist #2547, 15th April 2006
I have taken a pack of 10 cards numbered 1 to 10 and dealt them face down, giving a pair of cards to each of the clever kids Andy, Bandy, Candy, Dandy and Endy. They each look at their two cards and will, in turn, have to declare: “power” if the sum of the two is a perfect square or cube; “prime” if the sum is a prime; “big” if the sum is more than 12; “consecutive” if the two numbers are consecutive. For example, if dealt the 4 and 5, at his turn the child would make two declarations: “power” and “consecutive”.
When I asked them in turn for their declarations I am told that Andy, Bandy, Candy and Dandy each have nothing to declare. At that stage Andy said that he knew one particular declaration that Endy was bound to make. Endy then announced how many declarations he was going to make. Then only Bandy and Candy could work out Endy’s pair.
What are Andy’s, Dandy’s and Endy’s pairs?