536 Puzzles and Curious Problems

388 Answers

number l. The secret is to place six of each of two letters, and five of each of

the remaining four, when we get our second diagram, with only four blanks.

A .B C D E F A B C D E F

.D F E B A C D E A F B c

E C D .B F C D A

B D C E 13 D C E

C. .B E D C A E B F D

E D C b E F .D C A B

462. THE TEN BARRELS

Arrange the barrels in one of the following two ways, and the sides will

add up to 13 in every case-the smallest number possible:

o

8 6

4 9 5

732

o

7 8

593

642

By changing the positions of the side numbers (without altering the num-
bers contained in any side) we get eight solutions in each case, not counting
mere reversals and reflections as different.

463. LAMP SIGNALLING

With 3 red, white, or green lamps we can make 15 variations each (45).
With 1 red and 2 white we can make the same, 15, and each way will admit
of 3 variations of color order, 45 in all. The same with 1 red and 2 green,
1 white and 2 red, 1 white and 2 green, 1 green and 2 white, 1 green and 2 red
(270). With 1 red, 1 white, and 1 green we can get 6 by 15 variations (90).
With 2 red or 2 white or 2 green we can get 7 patterns (21). With 1 red and
1 white, or 1 red and 1 green, or 1 white and 1 green, we can get 14
variations each (42). With 1 lamp only we can get only 1 signal each (3).
Add together the numbers in parentheses (45,270,90,21,42, and 3), and we
get the answer, 471 ways.