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?
by Bill Kinally
Published Sunday August 13 2023 (link)
On her 11th birthday, Ann’s older brother Ben gave her a card on which he had drawn a 5×5 square grid with a different prime number in each of the cells. Every 5-cell row, column and diagonal had the same sum and, noting that 1 is not a prime, he used primes that made this sum as small as possible. The centre cell contained Ann’s age. All but one of the primes containing a digit 7 were on the two diagonals, the largest of these being in the bottom right corner. Two cells in the far right column contained a digit 5 as did two cells of the 4th row down. Four of the cells in the middle row contained a digit 3, and the largest prime on the grid was in the same column as two single digit primes.
What are the five prime numbers on the top row of the card?
by Howard Williams
Published Sunday August 06 2023 (link)
When I married, my wife insisted that everything be equally shared between us, which I readily agreed to, provided it included the gardening.
The garden is rectangular, with a smaller rectangular vegetable plot, of different relative dimensions, in one corner, the area of which is less than 7 per cent of that of the whole garden. The rest of the garden is lawned.
To satisfy my wife, I constructed the shortest straight length of partition that would split the garden in half, so that half the vegetable plot and half the lawn were each side of the partition. The length of the partition was 30 metres, which exactly equalled the perimeter of the vegetable plot. Both before and after partitioning, all side lengths were an exact number of metres.
What is the area of the lawn in each half?
by John Owen
Published Sunday July 30 2023 (link)
Our roulette wheel has fewer than 100 equal-sized sectors. Before each game a fixed number (fewer than half) of the sectors are randomly designated winning ones and the others as losing. A player can see which are the winning sectors, then is blindfolded. A ball is then placed at random in a winning sector and the player chooses to spin (S) the wheel or move (M) the ball clockwise by one sector. The game continues from there (the player has the same choices) and ends when the ball lands in a losing sector.
Alf’s longest winning run was MMSM while Bert’s was SSS and Charlie’s was MMMS. Being expert logicians, they had always chosen the option that gave the better chance of the ball landing in a winning sector. Remarkably, the probabilities of achieving each run of success were the same.
How many sectors are there and how many are winning sectors?
by Edmund Marshall
Published Sunday July 23 2023 (link)
A group of pensioners took a trip in a minibus, which had 11 seats for passengers, three on the back row, and two on each of the four other rows. The ages in years of the passengers were all different double-digit integers greater than 64, and for each pair of those ages there was no common factor other than 1. All seats were occupied, and, on any particular row of seats, the digits in the ages of passengers were all different. The sum of the ages of passengers on the back row was the largest possible with these conditions.
What was the age in years of the most elderly passenger sitting on the back row?