Sunday Times Teaser 3286 – Water Stop
by Howard Williams
Published Sunday September 14 2025 (link)
Chuck and his brother live on a long straight road that runs from west to east through their ranches. Chuck’s ranch is 13 km west of his brother’s. The two brothers often go from one ranch to the other on horseback, but go via a nearby river so that their horses may be watered. The shortest route via the river consists of two straight sections, one being 11 km longer than the other. The point at which they reach the river is 6 km north of the road.
What is the total length of the route between the ranches that goes via the river?
by Bernardo Recamán
Published Sunday September 07 2025 (link)
“How old are your five daughters?” Ignacio asked me.
“Considering their ages as whole numbers, they are all under 20, some of them are the same, and they add up to a prime number,” I answered. “Also, if you were to choose any two of them, no matter which two, their ages would have a common divisor greater than 1.”
“I can’t work out how old they are,” complained Ignacio.
“And you still couldn’t even if I told you the sum of all the ages. However, if I told you how old the youngest and oldest are, then you would be able to work out all the ages,” I responded.
“That’s great, because I now know how old all your daughters are!” Ignacio joyfully said after a pause.
In increasing order, what are the five ages?
by Andrew Skidmore
Published Sunday August 31 2025 (link)
We recently played a thrilling cricket match against the league leaders. Each team had two innings alternately (our opponents going first) and the combined total of runs scored in each innings determined the winner. Curiously both our opponents’ scores were 3-figure squares, the six digits all being different. The total of those two scores was also a square.
After our first innings (in which we scored a 3-figure prime number of runs), we had a lead, but after their second innings we trailed by a 3-figure prime number (less than 250). The six digits in these two primes were all different. Our second innings score was also a 3-figure prime number but we lost the match by a prime number of runs.
How many runs did we score in our second innings?
Sunday Times Teaser 3283 – Die Hard?
by Victor Bryant
Published Sunday August 24 2025 (link)
I have three identical standard dice (1 to 6 spots on each face, with 1 opposite 6, 2 opposite 5 and 3 opposite 4). I have placed them together in a row on a table and looked at the row from various sides. Regarding each face of a die as a digit (so that, for example, five spots would be regarded as a 5), I can read three 3-figure primes; one along the front of the row, one (the largest of the three) along the top of the row, and one along the back of the row viewed from behind. Furthermore, the total number of spots on the 11 visible faces is also a prime.
What, in increasing order, are the three 3-figure primes?
by Colin Vout
Published Sunday August 17 2025 (link)
For one composition, Skaredahora labelled the 12 notes in a standard octave from O to Z in some order, repeating cyclically. Each chord comprised four notes and had the same interval pattern: this meant the successive intervals between notes, when starting at the lowest note, ascending, and finishing with the addition of a note an octave above the lowest. The intervals all exceeded 1 and never increased. For instance, if the notes in an octave in ascending order were OQSYTVWXRPZU, then a chord of QWXZ would have an interval pattern of 5,1,3,3, which would fail for two reasons (an interval of 1 and an increase from 1 to 3).
His chords (with notes in random order) were QPWR, WVQO, RXQS, VYRO, STUP and UVYW.
Starting from O, what are the notes of the octave in ascending order?
Sunday Times Teaser 3281 – Square Dates
by Richard England
Published Sunday August 10 2025 (link)
Each year when I get my new diary, I like to look at the dates to see if they have any interesting properties. When I looked at this year’s diary, I was pleased to find two dates that are “square” in the following way. If the date is expressed with one or two digits for the day (ie, no leading zero is allowed), followed by two digits for the month and then the year in full, then 1.09.2025 is a square date, since 1092025 is the square of 1045.
The only other square date this year is 27.09.2025, since 27092025 is the square of 5205.
Using the same method of expressing the date, what is the first square date after 2025?
by Peter Good
Published Sunday August 03 2025 (link)
Clark had a set of more than one identical six-sided dice, and each die had a different positive whole number on each face. He would roll the dice and work out the total of all the numbers showing on the top faces. Clark knew that the largest possible total was 69, but it took him much longer to realise that it was impossible to roll a total that was a perfect square. The latter was true no matter how many of the dice were rolled.
In ascending order, what were the six numbers on each die?
by Stephen Hogg
Published Sunday July 27 2025 (link)
The Holmes’s new maths tutor, Dr Moriarty, wrote several two-figure by three-figure whole number multiplications on the board (with no answer repeated). Young Sherlock whispered to his brother, “That first one’s a doddle and the three-figure number is prime.” Mycroft replied, “Yes, it is a doddle, but the answer is also a DODDLE.” Sherlock looked puzzled. Mycroft explained that a DODDLE is a number with “Descending-Order Digits left to right — all different — DivisibLe Exactly by each digit.” Mycroft continued, “All of the above applies to the second multiplication as well.”
Sherlock noticed that just one other answer, to the final problem, was a DODDLE, with the three-figure value being odd, but not prime.
What is the answer to the final problem?
Sunday Times Teaser 3278 – Page Weight
by Mark Valentine
Published Sunday July 20 2025 (link)
An A5 booklet is produced by printing the pages onto sheets of A4 (both sides), then binding and folding along the middle. The booklet contains two chapters. The longer first chapter runs to 34 pages.
The pages in each chapter are numbered sequentially from 1 upwards. The front cover is page 1 of chapter one. Page 1 of chapter two follows directly after page 34 of chapter one. Any blank pages at the end of the booklet are not numbered.
Without changing their order, the sheets can be split into two piles, where the sums of the page numbers in each pile are equal.
How many pages does the second chapter have?
by John Owen
Published Sunday July 13 2025 (link)
Our non-standard croquet lawn has six hoops, at positions A to F, and a central peg at P. The equipment storage box is in the southwest corner at S, and the lawn is symmetrical in both the east-west and north-south directions. The diagram is not to scale, but D is south of the projected line from S to E. Also AB is half the width of the lawn. When setting out the equipment, I walk along the route SEFDPCBAS. All of the distances on my route between positions are whole numbers of feet (less than 60), and both D and E are whole numbers of feet north of the south boundary.
What is the total distance of my route?