A Brain Teaser: [Grains of rice]
From The Sunday Times, 21st December 1952 [link]
An Eastern potentate, at the end of a game of chess with his professional chess player, broached the delicate question of a reward for his many years of service.
The old man pointed to the board and said: “Suppose we number the squares from 1 to 64, thus. Your Majesty will observe that your King is on a lower-numbered square than mine. Pay me, I humbly beg, in grains of rice, for each square as many as the number of that square raised to the power of the number of the square occupied by your King, finishing at and including the square occupied by my King”.
“But that will be ruinous”, protested the monarch. “Not so, for the sum total contains but nine figures”.
“Then be it so. But will you take payment to the nearest thousand?”. “Certainly”, replied the sage, since if your men count accurately, I shall thereby forfeit only eight grains of rice”.
What squares were occupied by the two Kings, and how many grains were the old man’s reward?
This one of the occasional Holiday Brain Teasers published in The Sunday Times prior to the start of numbered Teasers in 1961. Prizes of 3 guineas and 2 guineas were offered.
This puzzle was originally published with no title.
[teaser-1952-12-21] [teaser-unnumbered]
S2T2 
Jim Randell 10:32 am on 23 January 2022 Permalink |
If the king is on square k, and the old man is on square j then the total number of grains t is given by:
This Python program runs in 52ms.
Run: [ @replit ]
from enigma import (irange, ndigits, printf) # consider the king's square for k in irange(1, 63): # t = total number of grains # j = old man's square t = j = 0 while j < 64: j += 1 t += j**k n = ndigits(t) if n > 9: break # check conditions if n == 9 and k < j and t % 1000 == 8: printf("k={k} j={j} t={t}")Solution: The kings are on squares 5 and 32. The reward consisted of 196,171,000 grains of rice.
The actual total being:
A grain of rice weighs approximately 1/64 gram, so the total prize would be just over 3065 kg of rice.
LikeLike