By Dominic Olivastro
Match wits with the nice minds of the world’s maximum civilizations during this attention-grabbing choice of old conundrums, brainteasers, and mind-benders.
• What do prehistoric bone markings and smooth machine technological know-how have in common?
• What is the secret of pi that stumped generations of old mathematicians?
• What are the traditional puzzle origins of renowned video games akin to tic-tac-toe and chess?
• Can you resolve the puzzles posed to emperor Charlemagne via Alcuin of York?
• What’s the key lore in the back of magic squares that captured the mind's eye of chinese language emperors, Persian mystics, and Benjamin Franklin?
Dominic Olivastro offers a well-liked background of arithmetic via concentrating on the puzzles that civilizations posed for his or her personal schooling and leisure. listed below are vintage “puzzle difficulties” from historic Africa, Egypt, Persia, China, and Greece and from cultures and texts spanning the center a while and the Renaissance all of the strategy to the present.
each one puzzle is associated with insightful folks and medical heritage that is helping make clear the mysterious function and foundation of the matter. interesting clues for realizing solutions draw on smooth problem-solving concepts and bring about old secrets and techniques that, prior to now, have infrequently been understood. even if you decipher them for his or her historic importance, classical knowledge, or simply for the sheer, maddening enjoyable of it, those pleasant puzzles offer a different, interesting, and enlightening advisor to the evolution of the human brain.
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Extra info for Ancient Puzzles: Classic Brainteasers and Other Timeless Mathematical Games of the Last Ten Centuries
Thus, to the Egyptians, the fraction be written 3/297 1/99. If you look at the fractions we started with each step of the way, you'll find something interesting: The fractions were 5/1, 4/33, and 3/297, in which the numerators (5, 4, 3) always decrease. Sylvester showed that this will always be the case, and thereby proved that the procedure always comes to an end since ultimately nothing of the fraction will be left over. THE ENTRANCE INTO ALL OBSCURE How did we find the unit fractions above? We wanted to find the largest unit fraction that did not exceed 5/n .
One-third of 15 is 5, which we subtract out ("Lo! 5 goes out"), and the remainder is 10. " Of course, this type of problem has been very popular through the ages. A parlor game mentioned by Fibonacci in the Liber Abaci is actually a very clever variation of a "think-of-a-number" problem: Guests are seated in a row. One of them is wearing a ring, although the host does not know who, nor does he know which hand, which finger, or which joint the ring is on. The wearer is told to count his position in the row, double it, add 5 to the product, multiply the sum by 5, and add 10.
So then, let us assume instead that the difference is not 1 but 2. This gives us a progression of 1, 3, 5, 7, 9. But now the two smallest terms sum to 4, and 1/7 of the three largest terms is 3. These are still not equal, but now they differ only by 4 - 3 = 1. " Now, 12/7 divided by 2/7 equals 41/2. That is what we add to 1, and thus get 51/2, the very number that Ahmes used in his solution. This is not quite the same as a regulafalsi, but the idea behind it is very similar. Why did Ahmes not say he found the number this way, if in fact he did?
Ancient Puzzles: Classic Brainteasers and Other Timeless Mathematical Games of the Last Ten Centuries by Dominic Olivastro