Year 1972- Volume 8
2020 - Present

Regrettably there were three major typographical errors in this issue, which are corrected below.

Keith Burns

In Vol 7 No 2 of Parabola, the following problem was set: A chess king is placed at the south-west corner of a chessboard.

Robert Kuhn

Robert Kuhn of Sydney Grammar has sent in the following attempted proof of this famous undecided conjecture.

Graham de Vahl Davis

In Parabola, Vol. 7 No. 3, an example was given of the use of the computer to solve the problem of finding all integers less than some upper limit which can be represented as KKK (written in base J>K) in two different ways.

Rod James

This is a new section in Parabola in which we intend to introduce you to some new games (both old and new) which have a mathematical flavour.

Across:

All the digits are different and odd

In Parabola Vol 7 No 1, Question 3 in the Senior Division of the 1970 Mathematics Competition states:

"Mathematical Puzzles and Diversions" and "More Mathematical Puzzles and Diversions" by Martin Gardner.

The "Four 4's" question last year provoked so much interest that we have decided to dig up a few more "research problems", i.e. questions which may have no final answer but where you can try to get as far as possible.

J171 Prove that for $n>2$$n>2$,$\left(n!{\right)}^{2}>{n}^{n}$$(n!)^2 > n^n$.

J161 Find a whole number, N, satisfying the following conditions:

(a) N is the product of exactly four distinct prime numbers.

John Rice

In Figure 1, there are four different surfaces: the sphere, the cylinder, the torus, and the Mobius strip. I expect you are familiar with the first two of these.

R. James and P. Donovan

Once again we are presenting a game for you to play (and maybe to analyze).

Across:

1. Each digit is larger than the one before it and only one of them is odd.

Judging from the lack of responses to the "Sums of Squares" last time, most readers must have had some trouble with it.

This question seems to be creating some interest among our readers.

Find two positive integers x,y so that xy=x+y

The sum of the numbers in a corridor (A Table of Corridors and Squares, Vol 8 No 1) can be represented as follows

J181 Show that the product of 4 consecutive integers is always one less than a perfect square.

J171 Prove that for $n>2$$n>2$,

$\left(n!{\right)}^{2}>{n}^{n}.$

J. Blatt
The system which we consider consists of a pendulum bob of mass m
connected by a rigid rod of negligible mass to the pivot. This system is illustrated in Figure 1.

D. J. Wilson
There is a fundamental difference between games of chance, such as roulette or two-up, and games of skill, such as poker or chess, which is shown by their description.

Joe Goozeff

I want to talk about intelligent machines.

Maharaja In this version of chess, one player has the usual sixteen chessmen and the other player has just one piece called the "Maharaja".

In issue 3 of 1971 you have a short note about a card with "The statement on the back of this card is false," printed on either side.

R. James

Because of the fact that the last issue of Parabola was so late, we only have one entry as yet to the questions you were left with in that issue.

"Puzzles in Math and & logic" by Aaron J. Friedland

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.

J181 Show that the product of 4 consecutive integers is always one less than a perfect square.