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? ... Hint ... Solution

The prisoner sat alone in his cell staring through the bars at the six doors to the guardroom beyond them. Suddenly, there was the sound of footsteps. One guard came in through door A and a second entered through door F. They unlocked the cell door. "We shall set you free," said one of the guards, "but first you must pass through all six doors, each door once only, in the correct order. Three are entrances only and three are exits only. Door A must be followed by door B or E; B by C or E; C by D or F; D by A or F; E by B or D; and F by C or D." With that the guards left through door B. In what order must the prisoner pass through the doors? ... Hint ... Solution

In the Dark Ages, in a remote part of Scotland, there once lived a 14-foot giant called Scrambo who used to terrorize the villagers by chasing them with his stick. They were so scared of him that when he ordered them to build a small castle for him to live in they quietly agreed. Fortunately for the villagers, Scrambo was rather stupid, and he chose flat land for his castle rather than the usual high ground. An annular moat was dug around a central circular region and the excavated soil was evenly distributed over the central region. There it was flattened to its original density to make a platform for the castle, raised above ground level. The buckets of soil were hauled from the moat with the aid of three wooden poles which spanned the moat (shown right). Each pole was three times the height of the giant and each just touched the central region and intersected another pole at the outer circumference of the moat.

The vertical distance D from the bottom of the moat to the top of the platform was exactly equal to that part of a pole spanning the moat. When one end of a pole was seated halfway across the flat moat bottom the other end just reached the top of the platform (i.e. the pole forms the hypotenuse of a right-angled triangle in a vertical plane, the height of which is D). What was the width and depth of the excavated moat? ... Hint ... Solution

Weedy Willie was getting too old to work the land alone so he decided to divide his cornfield between himself and his four sons in proportion to their five work rates. He knew that Rastus, Wig, Twig and Swig together could plant a field of corn in five hours whereas Wig, Twig and Swig and himself together could manage the same task in six hours. So Weedy divided his field into a two-digit square number of parts and kept just one part for himself. Now, Wig, Twig and Swig were identical triplets so each received the same whole number of parts. How many parts did each son get? ... Hint ... Solution

Professor Brainbloom had a very curious mathematical garden. There were probability trees, random flowers that had grown from seed, and broken garden gnomes that looked fractionally vulgar! Mathematical phenomena used to occur too. Like the time when the professor was laying a path of square slabs. He was just lowering the last slab into position when a prime pear struck his head. The slab crashed to the ground and shattered into pieces. The professor might have been annoyed, but he soon realised that the square slab had broken into exactly nine triangular pieces so that every angle was less than a right angle. How were the triangles arranged in the square? ... Hint ... Solution

As Sad Sally passes the town hall clock each day at noon, she looks at the clock and changes her watch to 12:00:00 (hours:minutes:seconds).She then goes home, and for want of something better to do, she listens out for the clock chimes. She believes that the single chime she hears at regular intervals occurs each hour on the hour and that since her watch must be wrong, she alters it accordingly. In reality, her watch runs at the same rate as the town hall clock, but the clock chimes on each occasion the hour and minute hands point in the same direction. What time is it on Sally's watch when she passes the town hall clock? ... Hint ... Solution

Said Alf to Bert, "The last time we met, our ages were both prime numbers, and when I was a quarter of the age I am now, you were that age plus half the age your father would have been thirty years previous to when he was six times the age you would have been when I was half your age". Said Bert to Alf "I'm off down the pub". How old were Alf and Bert the last time they met? ... Hint ... Solution

Postman Nat delivered all 10 of his letters in Ten-on-Sea to four single-occupier cottages. Of the four numbers delivered, Tom and Nap received the only pair that differed by the number of letters the postman had after completing his delivery, no two cottages receiving the same number. How many letters did Stan receive? ... Hint ... Solution

As Captain Klot stepped out of his spacecraft, he was welcomed by five Tiddlybons, the residents of Sigma 2. Knowing that the population had a precise hierarchy, Klot asked five questions to try to discover their ranking order. To help identify them, he stuck a letter on each one. Then he asked : Was A higher than C? Was B higher than E? Was C higher than D? Was D higher than B? Was E higher than A? For each question, the second (letter) mentioned whispered a "yes" or "no" to the first (letter) mentioned who reported "yes" or "no" to Klot. However, exactly two of the five lied consistently, both in whispering and reporting answers. If all had given truthful answers, their order would have been completely determined. However, precisely two reported answers did not correspond to the true hierarchy. The reported answers were "no", "no", "yes", "no", "no", respectively. The only Tiddlybon Klot could be sure to trust reported a correct answer. What was their ranking order and who lied? ... Hint ... Solution

Tom Bodger was an eccentric to the last and when he died he left precise instructions with his lawyer regarding the amount of money his only son should receive. The old man had devised a test for his son which would determine his inheritance. The lawyer presented the son with six coloured boxes : two blue, two green, and two red, and was told that each box contained a sum of money. Two of the boxes contained $10000 each, two contained $15000, and two contained $25000. He was allowed to choose any two boxes of the same colour, the total contents of which would constitute his entitlement. To help him decide, each box had a statement engraved on it. The blue boxes stated that : 'Both a blue box and a red box contain $10000 each'; the green boxes stated that 'Both a green box and a blue box contain $25000 each"; and the red boxes stated that : 'Both a red box and a green box contain $15000 each'. Only one of the three statements was true, and the corresponding two engraved boxes contained the greatest total of the three possible pairs. What was the total contents of each pair? ... Hint ... Solution

In a shop storeroom stood a red box with a blue one nested inside (shown below). The fit was so exact that no space remained between the five pairs of box walls and the tops of the two boxes were level. Now, the manager had red phobia, so he ordered his assistant to paint the box a different colour. His assistant, however, had found that the red box also fitted tightly inside the blue box on all hidden walls, thus the colour red could largely be concealed except for a small protrusion. The width of a box wall was 2mm. How far did the red box protrude out of the blue? ... Hint ... Solution

The three bears were sitting down to eat their porridge. It should have been a happy family occasion, but it soon became apparent to everyone that something was wrong. "Who's been eating my porridge?" they all cried, but the fact was, they'd eaten each others'! Mummy Bear had eaten half the amount that Daddy Bear would have had left in his bowl if only he had eaten from his bowl and no-one else. Now, Baby Bear originally had 30 spoonfuls in his bowl, Mummy Bear had 60 and Daddy Bear had 90. Baby Bear had eaten half the amount that Mummy Bear would have had left in her bowl if only Daddy Bear had eaten from her bowl and had eaten one third of his actual total consumption. Daddy Bear had eaten the amount that Baby Bear would have had left if only Mummy Bear had eaten from Baby Bear's bowl and had eaten one third of her actual total consumption. How many spoonfuls of porridge had each bear eaten? ... Hint ... Solution

Ticktock Town has a clock which long resides in the memory of all who visit there. As shown above, the clock consists of 12 small identical circular plates, numbered and seated on a circle so that each touches both its neighbours. The clock also has a wheel that runs around the outside of the clockface, has the same radius as each of the small plates, and has its centre attached by a rod and spring to the minute hand. The spring keeps tension on the wheel in the direction of the clock centre so that as the minute hand rotates the wheel rolls along the outer contours of the 12 plates without losing surface contact. How many times does the wheel rotate with respect to the clock centre each hour? ... Hint ... Solution

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