PuzzlingInPython

by John Fletcher

Published Sunday February 23 2025 (link)

One evening, Sherlock Holmes challenges Watson and Mycroft to a game of Cluedo.

He places one each of the six “person” cards, six “weapon” cards and nine “room” cards into the murder bag, shuffles the rest and deals them out equally.

Mycroft sees his cards and says, “If I guessed what was in the murder bag now, my chance of being correct is one in an integer that is a power greater than two.”

“I’m saying nothing.” Watson replies. “I’d only give something away.”

“Commendably prudent”, Sherlock says, “but the same is true for you.”

Watson studies his cards, then looks agitated. “How could you know that?”

“Sherlock isn’t cheating.” Mycroft reassures him. “He didn’t even know how many person cards you’re holding.”

How many room cards is Mycroft holding?

by Victor Bryant

Published Sunday February 16 2025 (link)

I have a standard set of 28 dominoes with a number of spots from zero to six at each end, and each possible pair of numbers occurring once in the set. When two dominoes in a line touch, the two adjacent ends must have the same number of spots.

I started a line by placing one of the dominoes on a table. Then, in correct domino style, I placed another adjacent to it at the right-hand end. I continued in this way (placing each domino at either end of the line) until more than 14 dominoes were lined up. At each stage the total number of spots on the table was a different odd number less than 100. In fact, the last two totals were prime but the first two totals were not.

From the left, what were the first six dominoes in the line (in the form 1-4, 4-0, …)?

by Mark Valentine

Published Sunday February 09 2025 (link)

I have written down a set of whole numbers, each greater than 1 and less than 100. I have squared each number and written the answers down in a list. The list contains all of the digits from 0 to 9 precisely once. Interestingly, for any two of the numbers, there is no common factor other than 1.

Naturally the sum of the digits in the squared set is 45, but what is the sum of the digits in the original set of numbers that I wrote down?

by Peter Good

Published Sunday February 02 2025 (link)

In a large pan, James baked three identical circular pizzas whose radius was a whole number of cm (less than 75). He laid them on a platter so that one pizza overlapped the other two. The pizza centres formed a right-angled triangle, with sides that were whole numbers of cm. The two lengths of overlap and the gap between the two non-overlapping pizzas (all measured along the lines joining the pizza centres) were all whole numbers of cm and could have formed another right-angled triangle.

He baked a fourth, smaller, circular pizza and it just fitted inside the triangle formed by the centres of the other three. Even if you knew the radii of the pizzas, you couldn’t work out the size of those right-angled triangles.

What was the radius of the smallest pizza?

by Colin Vout

Published Sunday January 26 2025 (link)

Equations in an archaic number system have been discovered:

BBC + BC = CBA
ABA#AB + ABAACA = CCB
ACAAC * AAC = ACAABABA

One letter (shown as #) is unclear, and could be either A or B. Letters basically represented different positive whole numbers; they might appear in any order in a string, but could contribute positively or negatively. The letter that was rightmost counted as a plus, but otherwise its basic value was compared with that of its right neighbour: if larger, it would count as plus; if smaller, as minus; if the same, then the same sign as that neighbour. (This works for interpreting Roman numerals too, eg, VII = 5+1+1 = 7, and XLIX = -10+50­-1+10 = 49.)

What are the basic values of A, B & C, in that order?

by Danny Roth

Published Sunday January 19 2025 (link)

George and Martha have five daughters; they are, in order of arrival, Andrea, Bertha, Caroline, Dorothy and Elizabeth. They now have ages that are all prime numbers in the range 28 to 60. The average is also a prime number, different from the other five.

Each daughter has a son, Adam, Brian, Colin, David and Edward respectively. They are all mathematics students, and are studying how to calculate square roots without using a calculator. One of them was given a perfect square with three or four digits (none repeated) and told to work out the square root. This he did accurately, getting his mother’s age, but he noted that the sum of the digits of that perfect square was also prime.

Which boy was it, and what is his mother’s age?

by Howard Williams

Published Sunday January 12 2025 (link)

I asked my daughter to find as many three-digit numbers as she could, each of which had the property that the number equalled the sum of the cubes of its individual digits. If she only found one such number, I asked her to give me this number — otherwise, if she had found more than one, to give me the sum of all such numbers found.

She gave me a prime number, from which I could see that not all answers had been found.

Which number or numbers did she not find?

by Michael Fletcher

Published Sunday January 05 2025 (link)

I have a piece of A6 paper on which I draw two triangles. The triangles are very similar in two ways. First of all, they are both the same shape. Not only that, the lengths of two of the sides of one of the triangles are the same as the lengths of two of the sides of the other triangle, but one triangle is larger than the other.

If the sides of the triangles are whole numbers of millimetres and the triangles don’t have any obtuse angles.

What are the lengths of sides of the larger triangle?

by Victor Bryant

Published Sunday December 29 2024 (link)

I have been testing for divisibility by numbers up to twelve. I wrote down three numbers and then consistently replaced digits by letters (with different letters used for different digits) to give

TEST TO TWELVE

Then I tested each of these numbers to see if they were divisible by any of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12. It turned out that each of these eleven divisors was a factor of exactly one of the three numbers.

What are the three numbers?

by John Fletcher

Published Sunday December 22 2024 (link)

In Cluedo, one “room” card (from nine possible ones), one “person” card (from six) and one “weapon” card (from six) are placed in a murder bag. The remaining 18 cards are shared out (four or five per player). Players take turns to suggest the contents of the murder bag. If wrong, another player shows the suggester a card, eliminating one possibility. The first person to know the contents of the murder bag will immediately claim victory.

My brothers and I are playing, in the order Michael-John-Mark-Simon. After several completed rounds, we all know the murder was committed in the Study. Michael and I know the murderer was Miss Scarlet with one of four weapons. Mark and Simon know the weapon and have narrowed it down to four people. Being new to Cluedo, we don’t learn from others’ suggestions.

From this point on, what are Michael’s chances of winning (as a fraction in its lowest terms)?

Post publication  clarification: Once a player knows the content of the murder bag they can declare immediately and do not have to wait their turn.