280 Answersget the seven cases: 24/1/24, 12/2/24, 2/12/24, 8/3/24, 3/8/24, 6/4/24,
4/6/24. One has only to seek the years containing as many factors as possible.- SHORT CUTS
To multiply 993 by 879, proceed as follows: Transfer 7 from 879 to 993,
and we get 872 and 1,000, which, multiplied together, produce 872,000. And
993 less 872 is 121, which, multiplied by the 7, will produce 847. Add the two
results together, and we get 872,847, the correct answer.
- MORE CURIOUS MULTIPLICATION
The number is 987,654,321, which, when multiplied by 18, gives
17,777,777,778, with 1 and 8 at the beginning and end. And so on with the
other multipliers, except 90, where the product is 88,888,888,890, with 90 at
the end.
[Dudeney overlooked such numbers as 1,001; 10,101; and 100,101 (made
up of I's and O's, with l's at the ends and no two consecutive I's), all of which
provide other answers.-M. G.)
- CROSS-NUMBER PUZZLE
The difficulty is to know where to start, and one method may be suggested
here. In reading the clues across, the most promising seems to be 18 across.
The three similar figures may be Ill, 222, 333, and so on. 26 down is the
square of 18 across, and therefore 18 across must be either III or 222, as the
squares of 333, 444, etc., have all more than five figures. From 34 across we
learn that the middle figure of 26 down is 3, and this gives us 26 down as the
square of Ill, i.e., 12321.
We now have 18 across, and this gives us 14 down and 14 across. Next we
find 7 down. It is a four-figure cube number ending in 61, and this is suffi-
cient to determine it. Next consider 31 across. It is a triangular number-that
is, a number obtained by summing 1,2,3,4,5, etc. 210 is the only triangular
number that has one as its middle figure. This settles 31 across, 18 down, 21
down, and 23 across. We can now get 29 across, and this gives us 30 down.