Answers 279- THE POSTAGE STAMPS PUZZLE
The number of postage stamps in the album must have been 2,519.- MENTAL ARITHMETIC
There are two solutions with numbers less than ten: 3 and 5, and 7 and 8.
The general solution to this problem is as follows:
Calling the numbers a and b, we have:a^2 + b^2 + ab = 0 = /a - mbj2 = a^2 - 2amb + b^2 m^2 •
... b + a = -2am + bm^2 ,
. b-a(2m+ I)
.. - m 2 _1
in which m may be any whole number greater than I, and a is chosen
to make b rational. The general values are a = m^2 - I and b = 2m + 1.
- SHOOTING BLACKBIRDS
Twice 4 added to 20 is 28. Four of these (a seventh part) were killed, and
these were those that remained, for the others flew away.
235. THE SIX ZEROS
100
330
505
077
099
1,111- MULTIPLICATION DATES
There are 215 different dates in this century complying with the conditions,
if we include such cases as 25/4/00. The most fruitful year was 1924, when we