## Enigma: No. 828 A line of boxes

2019-02-28 01:07:05

By Keith Austin LAST NIGHT I dreamt I went to Wanderley again. In my dream there was a line of boxes, stretching endlessly into the distance. The boxes were numbered 1, 2, 3 … in order and each contained at least one coin. Into my dream came Anna and Ravinder and they began to inspect the boxes. Ravinder would pick a box and then Anna would pick the box next to it whose number was one more than the number of Ravinder’s box. Ravinder would then look inn his box, count the coins and go to the box whose number was the number of coins. Finally they would each count the number of coins in the box they were standing by. They found that whichever box Ravinder chose at the start, and they checked every one in the line, Anna always had more coins than Ravinder. Answer each of the following questions, “Yes” or “No”. (a) Can such a line of boxes exist? (b) Is it possible that every box contains at least two coins? (c) Is it possible that there are at least two boxes each containing just one coin? (d) Can we say what are the numbers on the boxes with the smallest number of coins? (e) Can we say what is the number of coins in box number 1? (f) Can we say what is the number of coins in box 100? A £10 boook token will be awarded to the sender of the first correct answer opened on Thursday 27 July. The Editor’s decision is final. Please send entries to Enigma 828, New Scientist, King’s Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 822 was John Bacon of Sevenoaks. Answer to Enigma 822 All change at the top 1) City; 2) Albion; 3) City,