PuzzlingInPython

By Victor Bryant

Published 30th April 1995

In what follows, digits have been replaced by letters, a different letter being used consistently for each different digit. There are no zeros.

Each of the recurring decimals:

.ANDANDAND …
.NOWNOWNOW …
.NOTNOTNOT …
.ONEONEONE …
.ISISISIS …

equals a fraction with a denominator less than 50. And now not one is easy to find.

Please find what is DONE.

by Howard Williams

Published Sunday October 08 2023 (link)

My grandson likes to compile 3×3 magic squares, where each of the three rows of numbers, each of the three columns of numbers and both of the straight diagonals, add up to the same total. This he did without repeating any of the nine numbers in the square.

He has now progressed to compiling similar 3×3 squares, which instead of the eight rows, columns and diagonals of numbers adding to the same total, they instead multiply to produce the same product. In his first such square this product was 32,768. He was able to find every square of nine different whole numbers that gives this product, excluding identical rotational and mirrored squares.

What, in ascending order were the totals of the nine numbers in each of his different squares?

by Peter Good

Published Sunday October 01 2023 (link)

The rectangular snooker table had four corner pockets and two centre pockets (one each in the middle of the left and right sides, which were 12ft long). A ball always left the cushions at the same angle as it struck them. The cue ball was by the bottom right corner pocket and Joe hit it off the left cushion; it bounced off another seven cushions without hitting a ball or entering a pocket, then entered the right centre pocket. Four away!

Joe replayed the shot but the cue ball hit the left cushion further up the table than before, bounced another ten times without hitting a ball or entering a pocket, then entered the right centre pocket. Four away!

How much further up the table did the second shot hit the left cushion?

by Colin Vout

Published Sunday September 17 2023 (link)

When bad light ended the first day’s play, the total score was 182 with three batters having been “out” during the day.

In the successive stands, the lower-numbered and the higher-numbered batters scored in the ratios 7:3, 10:7, 1:11 and 11:19, in that order. The total score was the sum of the scores of the five batters.

The third batter was the highest scorer.

[In cricket the batting team starts with batters 1 and 2 together, and each is able to score. When one of them is “out” the third batter comes “in” to replace them, when one of that pair is out the fourth batter comes in, and so on. The amount by which the team score has increased while a particular pair is together is called the “stand”.]

What were the scores of all the batters, in their batting order?

by Stephen Hogg

Published Sunday September 10 2023 (link)

Grace mimicked Mr Dodgson: ‘’Take two different positive odd numbers with no shared prime factor. Multiply the larger by their sum, giving the perimeter of a distinct right-angled triangle with whole-number sides. Only such values and their multiples work.’’

Alice created a loop from part of a 1m thread. She was able to pull it tightly on a pinboard into a right-angled triangle with whole-number cm sides in two ways (with different-shaped triangles).

Alice then pulled the same loop tight over the thin polar spike of the classroom globe, down two meridians and along the equator. Thinking ‘’Logic’s dead!’’, she saw 90° equatorial angles and a non-zero polar angle, which obviously didn’t add to 180°.

Grace calculated the polar angle to the nearest degree. Curiously, transposing its two digits gave the globe’s whole-number centimetre radius.

Give this radius

by Victor Bryant

Published Sunday September 03 2023 (link)

There were eight people on the committee: four men — Jingo, King, Ling and Ming, and four women — Sheena, Tina, Una and Vina. They had to choose a chairperson from among themselves and so each of them voted for their choice, each person choosing someone of the opposite sex. Jingo’s choice’s choice was King. Also, Ling’s choice’s choice’s choice was Sheena. Furthermore, Tina’s choice’s choice’s choice’s choice was Una.

Just two people got fewer votes than their choice did. After further discussion the woman with the most votes was made chairperson.

(a) Who was that?

(b) Who voted for her?

by Victor Bryant

Published 13th February 2000


_ | 5 6 7 8 9
1 | ? ? ? ? ?
2 | ? ? ? ? ?
3 | ? ? ? ? ?
4 | ? ? ? ? ?


Imagine putting a digit into each of the 20 boxes of this grid so that, reading across, there are four five-figure numbers (labelled 1–4) and, reading down, five four-figure numbers (labelled 5–9). Do this in such a way that (naturally) the resulting numbers 1–9 have the following properties:

1, 4 and 9 are squares;
1 and 8 are cubes;
2, 3, 5 and 7 are primes;
6 is the product of two primes;
the average of 1–9 is more than 4.

You should then be able to answer the question:

What is the five-figure number forming 4 across?

by Andrew Skidmore

Published Sunday August 27 2023 (link)

Mrs Green uses a dice game to improve the maths skills of her pupils. The children sit four to a table and each child throws five dice. Points are awarded according to the sum and product for each child; bonus points are awarded if the five scores contain three or more of the same number.

At Liam’s table all four children had the same sum but all achieved that sum in different ways. Surprisingly, all of the twenty dice scored more than one and no bonus points were awarded. The distribution of scores was: sixes…5; fives…4; fours…2; threes…4; twos…5. Liam had the highest product.

What, in ascending order, were Liam’s five scores?