Enigma 1191: Sixth sense
30 November 2015
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From New Scientist #2347, 15th June 2002 [link]
Amber and Joe have a new game in which they each choose a whole number. Amber told me that she took two-thirds of Joe’s number away from 80 and then discarded any fraction to get her number. For example, if Joe chose 5 then Amber’s number was 76. Joe told me that he added three-quarters of Amber’s number to 23 and then discarded any fraction to get his number.
They asked me to blow the whistle for the start of the game and they each raised their hand when they had chosen their number.
Afterwards I pointed out they had not spoken to one another during the game; they smiled enigmatically.
What number did each one choose?