### by Danny Roth

#### Published Friday May 17 2024 (link)

George and Martha regularly read the obituaries in the national press; as well as the date of death, the date of birth of the person discussed is always shown. “That is interesting!” commented Martha as she looked at the three obituaries displayed one morning. Two of them have palindromic dates of birth (eg, 13/11/31, 21/6/12). “Very unlikely, indeed!” agreed George.

Assuming that birth dates are expressed as day (1-31), month (1-12) year (00-99), what is the probability of a palindromic birth date in the 20th century (1900 to 1999 inclusive), and will it be greater, equal or less in the 21st century?

### by Susan Bricket

#### Published Friday May 10 2024 (link)

A French farmer’s estate is shaped like a right-angled triangle ABC on top of a square BCDE. The triangle’s hypotenuse is AB, and its shortest side, AC, has length 1 kilometre. Nearing retirement, the farmer decides to sell off the square of land and, obeying the Napoleonic law of succession, divide the triangle into three equal plots, one for each of his two children and a third for him and his wife in retirement. His surveyor discovers, surprisingly, that his remaining triangle of land can be divided neatly into three right-angled triangles, all identical in shape and size (allowing for reflections / rotations).

How many hectares did the farmer sell? (1 hectare = area of 100m x 100m plot)

### by Andrew Skidmore

#### Published Friday May 03 2024 (link)

In our darts league, each team plays each other once. The result of each match is decided by the number of legs won, and each match involves the same number of legs. If both teams win the same number of legs, the match is drawn. The final league table shows the games won, drawn or lost, and the number of legs won for and against the team. The Dog suffered the most humiliating defeat, winning only one leg of that match. Curiously, no two matches had the same score.

What was the score in the match between The Crown and The Eagle?

### by Peter Good

#### Published Friday April 26 2024 (link)

Clark took a sheet of A4 paper (8.27 × 11.69 inches) and cut out a large square with dimensions a whole number of inches. He cut this into an odd number of smaller squares, each with dimensions a whole number of inches. These were of several different sizes and there was a different number of squares of each size; in fact, the number of different sizes was the largest possible, given the above.

It turns out that there is more than one way that the above dissection can be made, but Clark chose the method that gave the smallest number of smaller squares.

How many smaller squares were there?

### by Colin Vout

#### Published Friday April 19 2024 (link)

In retrospect it was inadvisable to ask an overenthusiastic mathematician to overhaul our local tram routes. They allocated a positive whole number less than 50 to each district’s tram stop. To find the number of the tram going from one district to another you would “simply” (their word, not mine) find the largest prime divisor of the difference between the two districts’ numbers; if this was at least 5 it was the unique route number, and if not there was no direct route.

The routes, each in increasing order of the stop numbers, were: Atworth, Bratton, Codford; Atworth, Downlands, Enford; Bratton, Figheldean, Enford; Downlands, Figheldean, Codford; Codford, Enford.

What were the route numbers, in the order quoted above?

### by Victor Bryant

#### Published Friday April 12 2024 (link)

I started with a six-by-six grid with a 0 or 1 in each of its 36 squares: they were placed in chequerboard style with odd rows 101010 and even rows 010101. Then I swapped over two of the digits that were vertically adjacent. Then in three places I swapped a pair of horizontally adjacent digits.

In the resulting grid I read each of the six rows as a binary number (sometimes with leading zeros) and I found that three of them were primes and the other three were the product of two different primes. The six numbers were all different and were in decreasing order from the top row to the bottom.

What (in decimal form) were the six decreasing numbers?

### by Howard Williams

#### Published Friday April 05 2024 (link)

I have three daughters and a grandson. They are all of different ages, with the eldest being younger than 35 years old, and my grandson being the youngest.

Three years ago the square of the age of my eldest daughter was equal to the sum of the squares of the ages of the other three. In another three years’ time the sum of the square of the age of my eldest daughter plus the square of the age of my grandson will be equal to the sum of the squares of the ages of my other two daughters.

In ascending order, what are their ages?

### by Mark Valentine

#### Published Friday March 29 2024 (link)

Every year Easter Bunnies must pass a series of demanding tests, the most important being the double jump. Rabbits perform a single jump comprising two hops, with the total distance scoring. For both hops, Max knows he has an equal chance of jumping any distance between two limits. For the first hop, the limits are 80 and 100cm. For his weaker second hop, these limits decrease but keep the same proportion.

However, the instructors have increased the required standard from 152 to 163cm. Max is worried; he can still pass, but his chance is half what it was before.

What, as a percentage, is his chance of passing this year?

### by J S Rowley

#### Published 28th January 1968 (link)

Some years ago the Bell family were holding their usual annual special birthday party. Four members of the family, of four different generations, had birthdays on the same day of the year. They were old Adam, his son Enoch, Enoch’s son Joseph and Joseph’s son David. On this occasion David remarked that the sum of any three of their four ages was a perfect square

Some years later old Adam died on his birthday, but it so happened that on the very same day David’s son Samuel was born, and the annual party was continued in subsequent years.

In 1967 at the usual party Samuel made exactly the same remark that David had made, on the previous occasion.

In what year did Adam die and how old was he then?

(Perhaps I should mention that no one survived to be 100!).

### by Victor Bryant

#### Published Friday March 22 2024 (link)

Audley’s age is a two-figure number. He has that number of cards and on them he has spelt out the consecutive numbers from one up to and including his age, (“one”, “two”, etc) with one number on each card. Then he has arranged the cards in a row in alphabetical order. It turns out that two of the numbers are in the “correct” place; ie in the same place as if he had arranged the cards in numerical order).

If he had done all this a year ago, or if he repeated this whole exercise in a year’s time, there would be no card in the correct place.

How old is he?