226 Answers- THE PERPLEXED BANKER
The contents of the ten bags (in dollar bills) should be as follows: $1,2,4,
8, 16,32,64, 128,256, 4S9. The first nine numbers are in geometrical progres-
sion, and their sum, deducted from 1,000, gives the contents of the tenth bag.
- A WEIRD GAME
The seven men, A, B, C, D, E, F, and G, had respectively in their pockets
before play the following sums: $4.49, $2.25, $1.13, 57¢, 29¢, 15¢, and 8¢. The
answer may be found by laboriously working backwards, but a simpler
method is as follows: 7 + 1 = 8; 2 X 7 + 1 = 15; 4 X 7 + 1 = 29; and so
on, where the multiplier increases in powers of 2, that is, 2, 4, 8, 16, 32, and 64.- DIGGING A DITCH
A. should receive one-third of two dollars, and B. two-thirds. Say B. can dig
all in 2 hours and shovel all in 4 hours; then A. can dig all in 4 hours and shovel
all in 8 hours. That is, their ratio of digging is as 2 to 4 and their ratio of
shovelling as 4 to 8 (the same ratio), and A. can dig in the same time that B.
can shovel (4 hours), while B. can dig in a quarter of the time that A. can
shovel. Any other figures will do that fill these conditions and give two simi-
lar ratios for their working ability. Therefore, A. takes one-third and B. twice
as much-two-thirds.
- NAME THEIR WIVES
As it is evident that Catherine, Jane, and Mary received respectively $122.00,
$132.00, and $142.00, making together the $396.00 left to the three wives, if
John Smith receives as much as his wife Catherine, $122.00; Henry Snooks
half as much again as his wife Jane, $198.00; and Tom Crowe twice as much
as his wife Mary, $284.00, we have correctly paired these married couples and
exactly accounted for the $1,000.00.- MARKET TRANSACTIONS
The man bought 19 cows for $950.00, 1 sheep for $10.00, and 80 rabbits for
$40.00, making together 100 animals at a cost of $1,000.00.