Volume 9


What has one side and no edges? This isn't an impossible riddle but has an answer viz. the Klein Bottle.

Have you ever taken any two numbers, added the second to the first; written this down, added the result to the second number, written the result own, and so on?

If asked to find the area bounded by the parabola $y=x^2$ the $x$-axis and the line $x=a$, you would write, almost instinctively $$ \text{area } = \int_0^a x^2 dx = \frac{1}{3}a^3 $$

Soon after writing my previous letter to you, I noticed the error I had made in connection with numbers 7 and 9.

The folllowing people had sent correct solutions before the publication of this issue:

The game chosen for this issue of Parabola is played by two people on a $10 \times 10$ chessboard.

Most candidates did not understand the question so ruled themselves out of consideration.

"Mathematical Excursions" by H.A.Merrill

J221 Find a 2-digit number $AB$ such that $(AB)^2 - (BA)^2$ is a perfect square.

J211 The numbers 31,767 and 34,924, when divided by a certain 3 digit divisor, leave the same remainder, also a 3-digit number. Find the remainder.