by Howard Williams
Published Sunday November 27 2022 (link)
On rugby international morning, I found myself, along with eight friends, in a pub 5.8 miles from the match ground. We were enjoying ourselves, and so wished to delay our departure for the ground until the last possible minute. The publican, wishing to keep our custom for as long as possible, offered to help us get there by carrying us, one at a time, as pillion passengers on his motorbike.
We could walk at 2.5mph and the bike would travel at 30mph. We all left the pub together, and arrived at the ground in time for kick-off.
Ignoring the time taken getting on and off the bike, what was our minimum travelling time in minutes?
by Andrew Skidmore
Published Sunday November 20 2022 (link)
Our chess club is divided into sections, with each section having the same number of players. The two oldest members will soon be retiring from playing and we will change the number of sections. The number of sections will change by one and so will the number of players in each section, but all the sections will still have the same number of players. This will result in there being a grand total of 63 fewer matches per year if each member plays all the other members of their section once per year.
How many players are in each section at the moment?
by Edmund Marshall
Published Sunday November 13 2022 (link)
Just nine Prime Ministers held office in the Kingdom of Primea during the 20th century. No two Prime Ministers held office at the same time, none had more than one period in office, and the gap between successive Prime Ministers’ terms was never more than a month. Each held office for a period of time in which the number of whole years was a different prime number (eg holding office from 1910 to 1915 could cover four or five whole years) and no Prime Minister served for more than 30 years. Appropriately, they all took office in prime years, but there was no change of Prime Minister in 1973.
In which years during the 20th century did new Prime Ministers in Primea take up office?
by Victor Bryant
Published Sunday November 06 2022 (link)
Eight friends met at a party; their ages in whole numbers of years were all different. They were Alan, Cary, James, Lucy, Nick, Ricky, Steve and Victor, with Lucy being the youngest. For each of them the square of their age was a three-figure number consisting of three different digits. Furthermore, for any two of them, the squares of their ages had at least one digit in common precisely when their names had at least one letter in common.
In alphabetical order of their names, what are the eight ages?
by Stephen Hogg
Published Sunday October 30 202 (link)
Moriarty’s papers were alight. Holmes memorised a 3×3 grid of different 4-digit values in ascending order as illustrated, from A (lowest) to I (highest), noticing that one numeral wasn’t used. Three cells, isolated from one another (no corner or edge contact), held squares of squares. Three others, similarly isolated, held cubes of non-squares. The other three held squares of non-squares. Holmes told Watson these features, specifying only the lowest value. “Not square,” remarked Watson.
“True, and many grids match these facts. However, if I told you the positions of the squares of squares in the grid, you could deduce a majority of the other eight values (apart from the lowest one)” replied Holmes.
In ascending order, which values did Watson now know certainly?
by Colin Vout
Published Sunday October 23 2022 (link)
Skaredahora used three rhythmic patterns of quaver beats in a short, purely percussive, composition. His “Dotykam” rhythm has accents on beats 1, 4, 6, 7, 8, 10 & 11; “Kluc” has accents on beats 1, 8 and one particular beat in between; and “Omacka” has accents on beats 1, 2, 5, 6 & 10. Several percussion instruments are involved, each playing one of the three rhythms, but starting at different times. Overall the patterns overlap, with every beat in the composition being filled by an accent from exactly one of the instruments, and all the patterns finishing by the end of the composition.
What is the other beat of Kluc, and what is the order of appearance of the rhythmic patterns (eg DOOKD)?
by Peter Good
Published Sunday October 16 2022 (link)
An artist hammered thin nails from a pack of 40 into a board to form the perimeter of a rectangle with a 1cm gap between adjacent nails. He created a work of art by stringing a long piece of wire from one nail to another, such that no section of wire was parallel to an edge of the rectangle. The wire started and ended at two different nails, no nail was used more than once and the length of the wire was a whole number of cm. No longer wire was possible that satisfied the above conditions.
What were the dimensions of the rectangle and the length of the wire chain (in cm)?
Note: the original (later corrected) on-line version omitted the red text.
by John Owen
Published Sunday October 09 2022 (link)
I was recently studying a large map that showed all the towns and major roads in a country. Every town had at least one road leading to it and every road led from one town to another. The roads only met at towns and all joined together to make a network with lots of blank areas in between, which I happily coloured in, needing just four different colours.
I counted up the number of areas (excluding the area around the outside of the network) and the number of towns, and discovered that both numbers were prime. Also, when I took these two numbers with the number of roads, the three numbers together used every digit from 0 to 9 precisely once.
In increasing order, what were the three numbers?
by Susan Bricket
Published Sunday October 02 2022 (link)
My son, at a loose end after A-levels, asked me for a mental challenge. As we’d been discussing palindromes, I suggested he try to find an arrangement of the digits 1 to 9 with the multiplication symbol “x” to give a palindrome as the answer, and he came up with 29678 x 1453 = 43122134. I said: “Now try to find the smallest such palindromic product starting in 4, where the last digit of the smallest number is still 3”. He found that smallest product, and, interestingly, if he added the two smaller numbers instead of multiplying them, then added 100, he also got a palindrome.
What was the smallest product?
by Howard Williams
Published Sunday September 25 2022 (link)
Little Spencer saves 5p coins in a jar, and when they reach £10, deposits them in his savings account. He likes playing with the coins. In one game, after first turning them all heads up, he places them in a row on the table. Starting from the left, he then turns over every 2nd coin until he has reached the end of the row. He then again starts from the left, and this time turns over every 3rd coin. He repeats this for every 4th, 5th coin etc, until finally he turned over just one coin, the last in the row.
At the end of the game I could see that if Spencer had exactly 75 per cent more coins he would have an increase of 40 per cent in the number showing heads. However, if he had exactly 50 per cent fewer coins, he would have a decrease of 40 per cent in the number showing heads.
What is the value of his 5p savings?