Puzzles

Published on May 15th, 2013 | by Simi

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# Puzzle Challenge 4

This months puzzles have been provided by Zbigniew Michalewicz, Emeritus Professor at the University of Adelaide.

The winner of this months puzzle of the month will receive a copy of Zbigniew’s book and a \$50 voucher, to enter email full working to all puzzles to mpe@amsi.org.au  by 30 June. Entries will be judged on number of correct answers, originality and presentation of ideas.
#1 THE ANT

An ant is placed at one end of a rubber string; this rubber string is one kilometer long. The ant starts walking on the string towards the other end with constant speed of one centimeter per second. At the end of each second the string is stretched so its length is extended by additional kilometer.

Here we assume that the string can be stretched indefinitely and that the stretching is uniform. Units of length and time remain constant.
The question is, does the ant ever reach the end of the string?

#2 THE MUSHROOM SALE

A farmer sells 100kg of mushrooms for \$1 per kg. The mushrooms contain 99% moisture. A buyer makes an offer to buy these mushrooms a week later for the same price. However, a week later the mushrooms would have dried out to 98% of moisture content. How much will the farmer lose if he accepts the offer?

#3 THE SECRET LIFE OF SHERLOCK HOLMES

When the producers of the new show “The Secret Life of Sherlock Holmes” were casting for the part of the protagonist, three young actors applied for the job. They all gave exemplary readings and the producers were hard pressed to chose between them. The director did have a slight preference for Byron Bentley, who came closest to fitting the director’s image of what the great Holmes should look like, so it was decided to determine how Bentley compared to Holmes in the reasoning department.

The director obtained five identical handkerchiefs and, in front of the three applicants, wrote “Sherlock Holmes” on three of the handkerchiefs and “Professor Moriarty” on the other two. He then stood Bentley center stage and pinned one of the handkerchiefs on Bentley’s back. Next, one of the other applicants was told to stand behind Bentley and a handkerchief was pinned on his back. The second applicant could see the name on Bentley’s handkerchief but could not see the name on his own.

The third applicant was placed behind the other two, so that he could see the names on their handkerchiefs but neither they nor he could see the name on the handkerchief that was placed on his back. Bentley, of course, could not see any handkerchief. “The first one of you who can deductively determine the name on his own back will get the part,” the director announced. After a few minutes of silence, Bentley correctly asserted that he was Sherlock Holmes. How did he know? “Elementary, my dear student.”

#4 FIVE MEN AND A MONKEY

Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food. Piled them all together and then went to sleep for the night. But when they were all asleep one man woke up, and he thought there might be a row about dividing the coconuts in the morning, so he decided to take his share. So he divided the coconuts into five equal piles. He had one coconut left over, and he gave that to the monkey, and he hid his pile and put the rest all back together. By and by the next man woke up and did the same thing. And he had one left over and he gave it to the monkey.

And all five of the men did the same thing, one after the other: each one taking a fifth of the coconuts in the pile when he woke up, and each one having one left over for the monkey. And in the morning they divided what coconuts were left into five equal piles and one left over coconut went to the monkey. Of course, each of the men must have known there were coconuts missing, but each one was guilty as the others, so they didn’t say anything. How many coconuts were there in the beginning?

At the end of a trial an eccentric judge sentenced the accused individual to some number of years in prison. However, the judge pointed out that this individual should “select” the number of years to serve by himself! The judge placed 12 boxes on the circumference of a circle. Each box was numbered, the clockwise sequence of numbers on the boxes was: 7, 10, 1, 3, 6, 11, 8, 4, 5, 9, 0, and 2.

The sentenced man was told that there is a number of coins in each box; again, the clockwise sequence of numbers of coins was 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The sentenced man should select a box and the number of coins in the box would determine the length of his sentence.

However, before the man pointed to any box, he asked the judge whether he can get any additional information, namely, how many boxes have numbers which exactly match the number of coins they contain? The judge replied that such information could not be disclosed, as it would allow him to determine the empty box. The man thought a little and pointed to the empty box anyway! How did he know? Which box did he point to?

Zbigniew Michalewicz, is an entrepreneur, author and professor who is recognized internationally as an mathematical optimization and new technologies expert. He is the author of Puzzle Based Learning.

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