Enigma 279: Tall stories
From New Scientist #1426, 18th October 1984 [link]
I’ve just been taking to four interesting sisters. I asked the youngest how old she was. She whispered the answer to the tallest sister who whispered the answer to Anita who told me the answer was 53. I was a bit surprised and so I assumed that one of those three must have made a mistake. So I asked the eldest how old she was. She whispered the answer to Barbara who whispered the answer to the shortest who told me the answer was 26! Had these three made a mistake?
Charlotte then explained to me that although all four of them knew their facts and did their calculations correctly, before stating a number they always changed it. One of the sisters always doubled her numbers, one always added 1, one always reversed the digits, and one always squared her numbers and deleted the left-hand digit of that square.
The second eldest sister said she’d help. She asked the eldest and youngest their ages (and the eldest’s answer was the larger of the two) and she calculated the difference and told me what it was: I happened to know that this was also her age.
Then the youngest whispered her age to Davina who whispered it to the second tallest who told me.
What number did she tell me?