PuzzlingInPython

by Peter Good

Published Sunday October 05 2025 (link)

Jack has a set of 28 standard dominoes: each domino has a spot pattern containing 0 to 6 spots at either end and every combination ([0 0], [0 1] and so on up to [6 6]) is represented in the set. He discarded a non-blank domino and arranged the remaining dominoes into six “groups”, each of which contained a positive cube number of spots; a group might comprise a single domino. He then discarded another non-blank domino and rearranged the remaining dominoes into six groups each of which again contained a positive cube number of spots. He managed to do this the maximum possible number of times.

How many dominoes did Jack discard, and how many spots in total were there on the dominoes that remained at the end?

by Henry C Warburton

Published Sunday September 28 2025 (link)

Todd privately tells each of four of his friends a letter of the password to his phone. All their letters have a different position in the password, but they do not know the position of their letter. He gives them all a list of 12 possible passwords, one of which is correct:

STEW, BOYS, PANS, STIG, NILE, LEER, STEM, WERE, GEMS, STAB, TEST, SPOT

He asks them all in turn if they know the password, and they all say no. He repeats this and gets the same response a number of times until the first friend to be asked says yes, and the rest no. Upon announcing that the first friend’s letter is in the second half of the alphabet, they all say yes.

What is Todd’s password?

by John Owen

Published Sunday September 21 2025 (link)

A large circular sea, whose diameter is less than 300km, is served by a ferry that makes a clockwise route around half of the sea, serving the ports of Ayton, Beaton, Seaton and Deaton in that order, then back to Ayton. Deaton is diametrically opposite Ayton. Each of the four legs of its route is a straight line, two of them being the same length. The lengths of all of the legs are whole numbers of km, and they all happen to be square numbers.

In increasing order, what are the three different leg lengths?

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?

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?

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?