PuzzlingInPython

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?

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?

by Howard Williams

Published Sunday July 06 2025 (link)

Johann enjoys playing with numbers and making up numerical challenges for his elder brother Jacob. He has worked out a new challenge, which involves Jacob trying to find the whole-number square root of a six-digit number. He explained that the sum of its individual digits is exactly five times the sum of its first and last digits. To make it easier, he tells him that no number is repeated in the six digits, there are no zeros, and the last three digits are in descending numerical order.

What is the square root of the six digit number?

by Andrew Skidmore

Published Sunday June 29 2025 (link)

I have taken a number of playing cards (more red than black) from a standard pack of 52 cards and distributed them in a certain way in two piles, each containing both red and black cards.

A card is taken at random from the smaller pile and placed in the larger pile. The larger pile is shuffled; a card is taken at random from it and placed in the smaller pile.

There is a one in eight chance that the number of red and black cards in each pile will be the same as they were originally.

How many black cards in total were used?

by Colin Vout

Published Sunday June 22 2025 (link)

If you rearrange the letters of a word to form another word, it’s called an anagram. So I think that if you rearrange the digits of a number to form another number, it could be called an anarithm.

Some decimal numbers when expressed in two number bases have representations that are anarithms of each other. For instance, the decimal number 66 is 123 in base 7 and 231 in base 5.

I’ve recently been looking at numbers in base 8 and base 5 and found that it is possible to have a decimal number whose representations in base 8 and base 5 are anarithms of each other.

In decimal notation, what is the largest such number?

by Victor Bryant

Published Sunday June 15 (link)

Delia plays a game with a stack of different pieces of card. To shuffle the stack she deals them quickly into four equal piles (face-downwards throughout) — the top card starts the first pile, the next card starts the second pile, then the third starts the third pile and likewise the fourth. She continues to place the cards on the four piles in order. Then she puts the four piles back into one big stack with the first pile on the bottom, the second pile next, then the third, with the fourth pile on the top.

She is very pleased with her shuffling method because each card moves to a different position in the stack, so she decides to repeat the shuffle a few more times. However, this is counter-productive because after fewer than six such shuffles the cards will be back in their original order!

How many cards are there in her stack?

by Danny Roth

Published Sunday June 08 2025 (link)

George and Martha’s five daughters left home some years ago but have all moved into the same road, Square Avenue, which has 25 normally numbered houses. At Christmas last year, the parents drove to the road to visit but, with age rolling on, George’s memory was beginning to fail him. “Can’t remember the house numbers!” he moaned. “Quite easy!” retorted Martha, “if you remember three things. If you take the house numbers of Andrea, Bertha and Caroline, square each of them and add up the three squares, you get the square of Dorothy’s house number. Furthermore, the average of Andrea’s and Dorothy’s house numbers equals the average of Bertha’s and Caroline’s house numbers. Finally, Elizabeth’s house number is the average of the other four and could not be smaller.”

Which five houses got a knock on the door?

By Peter Good

Andrew was building a rhombus-shaped patio. He could have paved it with equilateral triangular slabs with 1ft edges, but he wanted a layout with a hexagonal slab in place of six triangular ones at various places. He considered two layouts that were symmetrical in two perpendicular directions:

Layout 1: every triangular slab touches the perimeter of the patio in at least one point.

Layout 2: each group of three adjacent hexagonal slabs encloses exactly one triangular one.

The triangular and hexagonal slabs come in boxes of 12, and Andrew chose layout 1 because he would only need a third as many boxes of triangular slabs as layout 2.

What length were the sides of the patio and how many slabs in total would be left over?

by Howard Williams

Published Sunday May 25 2025 (link)

Four ramblers came to a tunnel that they all had to travel through. The tunnel was too dangerous to travel through without a torch, and unfortunately they only had one torch. It was also too narrow to walk through more than two at a time. The maximum walking speed of each of the walkers was such that they could walk through the tunnel in an exact number of minutes, less than ten, which was different for each walker. When two walkers walked together, they would walk at the speed of the slower one.

They all managed to get through the tunnel and in the quickest possible time, this time being five sixths of the total of their individual crossing times.

In ascending order, what are their four individual crossing times?