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Puzzles

Published on September 1st, 2013 | by Simi

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# Puzzle challenge 6

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 31 October. Entries will be judged on number of correct answers, originality and presentation of ideas.

#1 TYING STRINGS

A person holds 6 strings in her fist, the ends protruding above and below. Another person would tie the six upper ends in pairs, choosing the pairs at random, and then tie the six lower ends in a like manner. The person who ties the ends wins the game if the tying procedure produces one large ring. What is the probability of winning the game?

#2 RUSSIAN ROULETTE

Two men play a game of Russian roulette with a gun. The gun has six chambers, where two bullets were placed in two adjacent chambers. After a random spin of the barrel, the first man puts the gun to his head and pulls the trigger. Click. Now it is the turn of the second man. What should he do to increase his chances of staying alive: to spin the barrel first or just pull the trigger?

#3 CARD GAMES

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.

#4 SEVEN-ELEVEN

One day a customer arrived at a 7-Eleven shop and selected four items. He then approached the counter to pay for these items. The salesman took out his calculator, pressed a few buttons, and said:

“The total price is \$7.11.”

“Why?” said the customer, who was amazed by this coincidence. “Do I have to pay \$7.11 because the name of the shop is 7–Eleven?

“Of course not!” replied the salesman. “I have multiplied the prices of these four items and I have given you the result!”

“Why did you multiply these numbers?” asked surprised customer. “You should have added them to get the total price!”

“Oh, yes, I’m sorry,” the salesman said. “I have a terrible headache and pressed the wrong button!”

Then the salesman repeated all the calculations (i.e. he added the prices of these four items), but to both of their great surprise, the total was still \$7.11. What are the prices of these four items? Believe it or not, there is a unique solution to this problem…

#5 DATE DILEMA

Which day of the week, Saturday or Sunday, appears more often as January 1st?

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.

The winner of this months puzzle of the month will receive a signed copy of Zbigniew’s book.

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