PuzzlingInPython

by Andrew Skidmore

Published Sunday November 16 2025 (link)

I have a map showing the location of four castles. All of the distances between the castles are different two-figure whole numbers of miles, as the crow flies. Alton is due north of Sawley; Derry is furthest west. Fenwick is due east of Derry. Alton and Derry are the shortest distance apart, while the distance from Alton to Sawley is the largest possible to comply with all the other information. Again, as the crow flies,

How far is a round trip of the castles (A to F to S to D to A)?

by Howard Williams

Published Sunday November 09 2025 (link)

With the school inspector scheduled to visit her school, Tina is taking extra care in preparing her lesson plan. The lesson deals with areas, shapes and symmetries. She has produced soft cards on which have been printed a four by four grid, and will ask the pupils to cut the grid into two shapes of equal area, but by only cutting along the lines. She wanted them to create as many different possible shapes in this way, explaining that two shapes are different only if you can’t make one the same as the other by rotating it, turning it over, or both. It turned out that the maximum number of different shapes was the same as the number of pupils in the class.

How many pupils are there in the class?

by Victor Bryant

Published Sunday November 02 2025

I have three granddaughters Jay, Kay and Elle. I set Jay and Kay a test and asked each of them to produce a list of positive numbers that used just nine digits with no digit occurring more than once. I wanted the majority of the numbers in each list to be odd and the majority of the numbers in each list to be perfect squares.

Jay’s list (which contained more numbers than Kay’s) added up to give the year of Elle’s birth, whereas Kay’s list added up to give the year in which Elle will be 25.

In one of the lists the highest number was a perfect square.

What (in increasing order) were the numbers in that list?

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?