Solutions to Brain-Twisters III


The solutions too will often involve the use of figures and tables. As in the puzzles page, the figures are in gif format and should be downloadable by text-based browsers like Lynx.


Solution to Puzzle #1

Each son rides the other son's horse.


Solution to Puzzle #2

No. Though each of the sons gets more than was specified by their father's Will, and though the camels happily escape mutilation, the Will itself has been violated, because it provided that 17/18 of a camel (i.e. 17 minus 17/2 minus 17/3 minus 17/9) was to remain after the divison between the sons. The Great Mosque (the residuary legatee) and anyone who believed that the term of the Sheik's Will should be strictly observed would be dissatisfied with the wise man's arrangement.


Solution to Puzzle #3

Not more than 4 questions will be necessary, but sometimes (in one case out of three) 3 questions will suffice.

1st question (addressed to the 1st banker): "If I asked you whether the 2nd banker is an equivocator (i.e. a person who sometimes tells lies and sometimes tells the truth), would you say yes?" If he answers yes, we know that the 3rd banker cannot possibly be an equivocator and we accordingly address our subsequent questions to him; if the 1st banker answers no, we know that the second banker is not an equivocator and we ask him our subsequent questions.

2nd question (addressed to the 3rd or the 2nd banker depending on whether the answer to the 1st question was yes or no respectively): "If I asked you whether the 1st banker is Albanian, would you answer yes?" If the answer is yes, the 3rd question (asked to the same person as the 2nd question) is: "If I asked you whether the 2nd banker is American, would you say yes?" By elimination, we know the identity of the 3rd banker also.

If, on the other hand, the answer to the 2nd question is no, two further questions will be required (a total of 4). 3rd question: "If I asked you whether the 1st banker is American, would you say yes?" If the answer is yes, we know that the 1st banker is American; if it is no, we know that he is Austrian. In either case we require one further question (the 4th question) to identify the two remaining bankers.

Since the 1st question 'eliminates' the equivocator, we know that the remaining questions are addressed to someone who is consistently honest or consistently dishonest; and the questions are so worded that the answers will be the same whether he is honest or dishonest. The moral is that consistently dishonest people are far more dependable than those who occasionally tell the truth.


Solution to Puzzle #4

The triangle shown has a base of 8 and sides of 5 and 3. Since 5+3=8, it is a triangle that has degenerated to a straight line. On this line the line segment labelled x has a length of 1.


Solution to Puzzle #5

Just turn the small triangle upside down:

Download this figure for Solution to Puzzle #5

It then becomes obvious that the large triangle consists of four of the small ones.


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Revised: November 30, 1996