### by Howard Williams

#### Published Sunday September 25 2022 (link)

Little Spencer saves 5p coins in a jar, and when they reach £10, deposits them in his savings account. He likes playing with the coins. In one game, after first turning them all heads up, he places them in a row on the table. Starting from the left, he then turns over every 2nd coin until he has reached the end of the row. He then again starts from the left, and this time turns over every 3rd coin. He repeats this for every 4th, 5th coin etc, until finally he turned over just one coin, the last in the row.

At the end of the game I could see that if Spencer had exactly 75 per cent more coins he would have an increase of 40 per cent in the number showing heads. However, if he had exactly 50 per cent fewer coins, he would have a decrease of 40 per cent in the number showing heads.

What is the value of his 5p savings?

### by Andrew Skidmore

#### Published Sunday September 18 2022 (link)

Liam has nine identical dice. Each die has the usual numbers of spots from 1 to 6 on the faces, with the numbers of spots on opposite faces adding to 7. He sits at a table and places the dice in a 3×3 square block arrangement.

As I walk round the table I see that (converting numbers of spots to digits) each vertical face forms a different three-figure square number without a repeating digit.

As Liam looks down he sees six three-digit numbers (reading left to right and top to bottom) formed by the top face of the block, three of which are squares. The total of the six numbers is less than 2000.

What is that total?

### by Mark Valentine

#### Published Sunday September 11 2022 (link)

At the local arcade, Claire and David played an air hockey game, consisting of a square table with small pockets at each corner, on which a very small puck can travel 1m left-right and 1m up-down between the perimeter walls. Projecting the puck from a corner, players earn a token for each bounce off a wall, until the puck drops into a pocket.

In their game, one puck travelled 1m farther overall than its left-right distance (for the other, the extra travel was 2m). Claire’s three-digit number of tokens was a cube, larger than David’s number which was trianglular (1+2+3+…). Picking up a spare token, they could then arrange all their tokens into a cube and a square combined.

How many tokens did they end up with?

### by Edmund Marshall

#### Published Sunday September 04 2022 (link)

I have a large number, fewer than 2000, of identical spherical bonbons, arranged exactly as a tetrahedral tower, having the same number of bonbons along each of the six edges of the tower, with each bonbon above the triangular base resting on just three bonbons in the tier immediately below.

I apportion all my bonbons between all my grandchildren, who have different ages in years, not less than 5, so that each grandchild can exactly arrange his or her share as a smaller tetrahedral tower, having the same number of tiers as his or her age in years.

The number of my grandchildren is the largest possible in these circumstances.

How many tiers were in my original tower, and how old in years are the eldest and youngest of my grandchildren?

### by Bill Kinally

#### Published Sunday August 28 2022 (link)

Next month’s four week rota for Monday to Friday dinner duties starting on Monday 1st is covered by five teachers each having the following duty allocations. Ann, Ben and Ed each have four, Celia six and Dave has two. Strangely, all the prime number dates (1 is not a prime) are covered by Ben, Celia and Dave, while the others are covered by Ann, Celia and Ed. After working a duty, nobody works on either of the following two shifts, so anyone working on a Friday will not work on the following Monday or Tuesday. Celia has no duties on Mondays while Ben and Ed have none on Wednesdays.

In date order, who is on duty from Monday to Friday of the first week?

### by Victor Bryant

#### Published Sunday August 21 2022 (link)

My five nieces Abby, Betty, Cathy, Dolly and Emily each had some sweets. I asked them how many they had but they refused to answer directly. Instead, in turn, each possible pair from the five stepped forward and told me the total number of sweets the two of them had. All I remember is that all ten totals were different, that Abby and Betty’s total of 8 was the lowest, and that Cathy and Dolly’s total of 18 was the second highest. I also remember one of the other totals between those two but I don’t remember whose total it was. With that limited information I have worked out the total number of sweets.

In fact it turns out that the other total I remember was Betty and Cathy’s.

In alphabetical order of their names, how many sweets did each girl have?

### by Stephen Hogg

#### Published Sunday August 14 2022 (link)

At Teaser Tor trig. point I found a geocaching box. The three-figure compass bearings (bearing 000=north, 090=east, etc.) from there to the church spires at Ayton, Beeton and Seaton were needed to decode the clue to the next location.

Each spire lay in a different compass quadrant (eg 000 to 090 is the North-East quadrant). Curiously, each of the numerals 1 to 9 occurred in these bearings and none of the bearings were prime values.

Given the above, if you chose one village at random to be told only its church spire’s bearing, it might be that you could not calculate the other two bearings with certainty, but it would be more likely you could.

Give the three bearings, in ascending order.

### by Colin Vout

#### Published Sunday August 07 2022 (link)

A gardener was laying out the border of a new lawn; he had placed a set of straight lawn edging strips, of lengths 16, 8, 7, 7, 7, 5, 4, 4, 4 & 4 feet, which joined at right angles to form a simple circuit. His neighbour called over the fence, “Nice day for a bit of garden work, eh? Is that really the shape you’ve decided on? If you took that one joined to its two neighbours, and turned them together through 180°, you could have a different shape. Same with that one over there, or this one over here — oh, look, or that other one.” The gardener wished that one of his neighbours would turn through 180°.

What is the area of the planned lawn, in square feet?

### by Nick MacKinnon

#### Published Sunday July 31 2022 (link)

A factory makes six types of cylindrical pipe, A to F in decreasing size, whose diameters in centimetres are whole numbers, with type A 50 per cent wider than type B. The pipes are stacked in the yard as a touching row of As with an alternating row of touching Bs and Cs in the next layer, with each B touching two As. Type Ds fill the gap between the As and the ground; Es fill the gap between As and the Bs; and Fs fill the gap between As, Ds and the ground. Finally another row of As is put on top of the stack, giving a height of less than 5 metres.

What is the final height of the stack in centimetres?

### by Angela Newing

#### Published Sunday July 24 2022 (link)

Five witnesses were interviewed following a robbery at the bank in the High Street. Each was asked to give a description of the robber and his actions. The details given were: height, hair colour, eye colour, weapon carried, escape method.

$\begin{array}{|c|c|c|c|c|c|}\hline \mathbf{Witness} & \mathbf{Height} & \mathbf{Hair\;Colour} & \mathbf{Eye\;colour} & \mathbf{Weapon}& \mathbf{Escape}\\ \hline \mathbf{one} & short & fair & brown & cricket\;bat & motorbike \\ \hline \mathbf{two} & tall & fair & grey & gun & car \\ \hline \mathbf{three} & tall & dark & brown & crowbar & motorbike \\ \hline \mathbf{four} & short & ginger & blue & knife & car \\ \hline \mathbf{five} & tall & dark & blue & stick & pusbike \\ \hline \end{array}$

When the police caught up with the perpetrator, they found that each of the five witnesses had been correct in exactly two of these characteristics.

What was the robber carrying, and how did he get away?