Year 1973- Volume 9
2020 - Present

If you went to Stockholm today, you would find in the middle of the city an "oval-shaped" pool about 200 meters long with fountains and a translucent base. Under this pool is a self-service restaurant with sunlight filtering through the pool and surrounded by shops.

G. Szekeres

In how many different ways can 4 be expressed as the sum of positive integers?

Doug Mackenzie

Two of the interesting problems related to chess are the number of queens needed to dominate a chess board and how few squares can be attacked by a given number of queens.

With regard to the case in "Research Corner" concerning number which can be written as the sum of three squares and four squares, all numbers of the form ${m}^{2n}\left(8k+6\right)$ $m^{2n}(8k+6)$ can only be written as the sum of at least three square numbers

This is a game which was invented by Piet Hein, although it was rediscovered in 1948 by John Nash in America.

"Number, the language of science" by T. Dantzig

J201 Find the last digit of 7 1001 ${7}^{1001}$ $7^{1001}$.

J191 A yacht starts from a point A, one mile due East of a buoy O, and tacks up to the buoy as indicated in the diagram.

K. Wilkins

The term "polyomino" is used to describe a set of squares, which are simply connected together by edges. The word "domino" used in this way refers to the shape of the playing dominoes, that is two squares simply connected along an edge.

When we do Euclidean geometry, we use the idea of congruence of triangles and we have certain rules for deciding whether two triangles are congruent or not.

Referring to the article by John Rice on Topology: Another fascinating aspect of topology is the bottle with one side that topologists have tried to construct. An example is sketched below.

As this section seemed to be so popular last year, we have decided to present another one.

K. Wilkins

The game this time is based on the article 'Polyominoes' on page 2 of this issue

Given a triangle with sides a,b,c and a segment of length d.

"The Great Mathematicians" by H.W. Turnbull.

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.

J201 Find the last digit of 7 1001 ${7}^{1001}$ $7^{1001}$.

Philip Diacono

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

Charles Cave

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 $y={x}^{2}$ $y=x^2$ the $x$ $x$-axis and the line $x=a$ $x=a$, you would write, almost instinctively

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:

K. Wilkins

The game chosen for this issue of Parabola is played by two people on a 10×10 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 $AB$ $AB$ such that $\left(AB{\right)}^{2}-\left(BA{\right)}^{2}$ $(AB)^2 - (BA)^2$ 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.