PuzzlingInPython

by Stephen Hogg

Published Sunday October 26 2025 (link)

My blood pressure was 160 systolic over 100 diastolic. I knew 120 over 80 is “normal”, so Doctor Hoo was concerned. She loaned me a TARDSI (Test And Record Diastolic Systolic Indicator) for a few days. I logged 12 blood pressure readings, comprising 24 different values (12 systolic between 120 and 160, and 12 diastolic between 80 and 100). I noticed some curious things about these values. Each systolic:diastolic pair had no repeated digits nor common prime factors. The systolic and diastolic sets each had exactly six odd values, but the lowest and highest values in each set were the only primes. No value was a digit rearrangement of any other and the systolic set had no consecutive values.

Give the systolic:diastolic pair you can be sure I measured (as SSS:DD eg 123:74)

by Danny Roth

Published Sunday October 19 2025

George and Martha are keen pop music fans. They recently followed the progress of one record in the charts and noticed that it was in the Top Ten for three weeks in three different positions, the third week’s position being the highest. In practice, a record never zigzags; it reaches a peak and then drops. For example, 5,4,9 or 5,6,9 are possible but 2,5,3 is not.

“That’s interesting!” commented Martha. “If you add the three positions, you get the day of the month when my father was born and if you multiply them, you get a number giving the month and last two digits of that year.” “Furthermore,” added George “two of the positions also indicate the last two digits of that year.”

What were the three positions in chronological order, and what was the date of Martha’s father’s birth?

by Colin Vout

Published Sunday October 12 2025 (link)

In our town centre the scheduled times taken for stages between bus stops are 5, 8 or 9 minutes. The only possible stages (in either direction) are between: stops Market and Castle; Market and Park; Market and Hospital; Station and Castle; Station and University; Castle and Park; University and Park; Park and Hospital.

Route 1 is from Market to Castle in 5 stages, which sum to 29 minutes; Route 2 is University to Market, totalling 19 minutes; Route 3 from University to Hospital takes 31 minutes for its 4 stages; Route 4 goes from University to Station in 27 minutes; Route 5 uses 4 stages to get from Market to University in 24 minutes. No route visits a stop more than once.

What are the stage times (in order) for Route 1, and Route 4?

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?