290 AnswersP Q Height Area
2 4 3 6
8 14 12 84
30 52 45 1,170
112 194 168 16,296
418 724 627 226,974
1,560 2,702 2,340 3,161,340Here three times the square of P, added to 4, will make the square of Q.
Every value of P is four times the last number less the previous one, and Q is
found in the same way after the first step. The height is half as much again as
P, and the area is the height multiplied by half of Q. The middle number of
our three sides will always be found as Q. The last line will give us the first case
where the area is divisible by 20. The triangle is 2,701, 2,702, 2,703, with
height 2,340.
- THE DONJON KEEP WINDOW
The illustration will show how the eight lights "whose sides are all
square window may be divided into equal." Every side of the pane is of
the same length.
It was understood ( though not
actually stated) that the lights should
be all of the same area, but the four
irregular lights are each one-quarter
larger than the square lights. And
neither the shape nor the number of
sides of the lights are equal. Yet the
solution strictly complies with the
conditions as given. If you shut out all
these tricks and quibbles in a puzzle
you spoil it by overloading the condi-
tions. It is better (except in the case
of competitions) to leave certain
things to be understood.