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?
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, while the rest were truthtellers, 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?
Giuseppe Peano, the Italian logician, was walking through Bratislava Wood humming Beethoven’s Piano Sonata No. 4, when he came upon a toll bridge that spanned a wide river. There he found a sign which informed him that to pass across the bridge he would need to pay four gold coins. Suddenly, Babette the elf appeared before him with three boxes, each with a number inscribed on it (shown left). “These three boxes contain a total of four gold coins,” said Babette, “but no box contains more than two coins.
No two adjacent boxes contain the same number of coins and only one box states the correct number of coins that can be found inside it. If you can deduce the distribution of the four coins among the three boxes then the gold coins are yours.” One might expect that logical problem solving would be a Peano forte, but the famous thinker had simply been dreaming it all and was therefore ill-disposed to write down his solution. Can you assist by stating the number of coins in boxes A, B, and C?
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Illustrations by Barry R. Clarke