TIME: - I HOUR
1. The Five Newsboys Puzzle. (6 marks)
Five clever newsboys formed a partnership and disposed of their papers in the following manner. Tom Smith sold one paper more than one quarter of the whole lot. Billy Jones disposed of one paper more than a quarter of the remainder. Ned Smith sold one paper more than a quarter of what was left, and Charley Jones disposed of one paper more than a quarter of the remainder. At this stage the Smith boys had together sold just one hundred papers more than the Jones boys had sold. Little Jimmy Jones, the youngest kid in the bunch, now sold all the papers that were left. The three Jones boys sold more papers than the two Smith boys, but how many more?
2. The Monkey and the Pulley (2 marks)
A weightless and perfectly flexible rope is hung over a weightless, frictionless pulley attached to the roof of a building. At one end is a weight, which exactly counterbalances a monkey at the other end. If the monkey begins to climb, what will happen to the weight - will it remain stationary, will it rise or will it fall?
3. The Damaged Engine (4 marks)
We were going by train from Bonston Village to Liberty Town, and an hour after starting an accident happened to the engine. We had to continue the journey at three-fifths of the former speed. It made us two hours late at Liberty Town, and the driver said that if only the accident had happened fifty miles farther on the train would have arrived forty minutes sooner. Can you tell from that statement just how far it is from Bonston Village to Liberty Town?
4. Order, Gentlemen, Order!? (6 marks)
Bob and Benjamin were excitedly describing the result of the First Annual Pickwickian Commemorative Wheelbarrow Race at Dingley Dell. Snodgrass, Tupman and Winkle had been the three contestants.
"Tupman won the race; Winkle was in second place," reported Bob. Benjamin disagreed. "It was Snodgrass who won. Tupman came second." In fact, neither Bob nor Benjamin had given a correct version of the result as each had made one true and one false statement. What was the actual placing of the three contestants?
5. The Round Table (8 marks)
Yesterday evening, Helen and her husband invited their neighbors (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following:
"Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna.
Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband.
Jim sat on the left of the woman who sat on the left of Roger.
I did not sit beside my husband."
Detailed solution
1 Solution: The Jones boys sold 220 more papers than the Smith boys. The original number of papers was 1,020.
2. Solution: As the monkey climbs, the weight will rise by the same amount.
3. Solution: The distance from Bonston Village to Liberty Town must be 200 miles. The train went 50 miles at 50 M.P.H. and 150 miles at 30 m.p.h. If the accident had occurred 50 miles farther on, it would have gone 100 miles at 50 m.p.h. and 100 miles at 30 m.p.h.
4. Solution: The order of the contestants is: Snodgrass, Winkle, Tupman.
5. Solution: From the second statement, we know that the six people sat at the table in the following way (clockwise and starting with Helen's husband):
Helen's husband, woman, man, woman, man, Esther
Because Helen did not sit beside her husband, the situation must be as follows:
Helen's husband, woman, man, Helen, man, Esther. The remaining woman must be Anna, and combining this with the first statement, we arrive at the following situation:
Helen's husband, Anna, man, Helen, Victor, Esther.
Because of the third statement, Jim and Roger can be placed in only one way, and we now know the complete order:
Helen's husband Roger, Anna, Jim, Helen, Victor, Esther.
Conclusion: the name of Helen's husband is Roger.
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