# mathematics puzzles

Tiny Tum's mathematics homework book was the untidiest in the class. In one of his equations, the two different arithmetic signs were missing. What is the unknown whole number x that balances the equation?

Sparky the electrician's apparatus consisted of 16 batteries labelled A-D and eight 10V bulbs mounted on a board. Each letter A-D represented a single-digit non-zero number of volts, though not necessarily four different values. A switch determined whether or not the circuits all ran horizontally or all vertically, so that each row/column of four batteries fully lit the bulb at the end of that row/column.

This meant that when the batteries were correctly arranged, either all columns or all rows of bulbs could be illuminated according to the switch position. One day, Plug the apprentice removed all the batteries and used just three of them to illuminate fully each bulb in turn. Unfortunately, he had replaced the 16 incorrectly (as shown) so that at least one bulb would blow both vertically and horizontally when connected. Luckily, Sparky was quite switched on and realised that he could rectify the situation by simply interchanging two batteries. What are the values A, B, C and D?

A medieval king needed to work out how he could recruit fighting men for the battle ahead. However, there were so many distractions around the castle, his thinking became confused. So in order to change his daze into knights, he asked for a secluded walk to be made so he could ponder in peace. The head gardener was given the job of planting lines of high bushes. First, he planted a line running 100 paces east. Then from the end of that line he planted a line 100 paces north, then 100 west, 98 south, 98 east, 96 north, 96 west, and so on. This made a square spiral path 2 paces wide. If the king intended to walk down the middle of the path, how long was the path?

"I've always been 45 years older than your Dad", said Grandma to young Trickle, "but now the two digits in my age, both prime, are the reverse of the two in your Dad's age". How old is Grandma?

"Hey Daddy," said Jill, "I'm feeling quite ill",

"Today, I'm not a well daughter",

So he bent to her will and went up the hill,

To fetch five units of water.

On reaching the well, he suddenly fell,

And shattered his pail on the road,

But spying two lasses with cylindrical glasses,

He saw how to carry his load.

They're negligibly thick, he saw rather quick,

Praising himself for sagacity,

And what made it right was that both had same height,

Though obviously different capacity.

Sixteen and four were their volumes to pour,

And Dad filled the first up with water,

The second had none, but purely for fun,

He still took it back to his daughter.

"Just tell me", snarled Jill, going in for the kill,

"How we measure out five with these glasses?

Five from sixteen, is a bit of a dream",

Dad wished he'd eloped with the lasses.

When the Chompem Cannibals of Drybone Island threw a dinner party six cannibals turned up and so they decided to eat each other in turn. Someone was selected for everyone to eat (except the victim!), and when he had been eaten, someone else was selected, and so on. If it took one cannibal two hours on his own to devour one person, how long was it before just one consumer remained?

Illustrations by Barry R. Clarke