| PUZZLE CORNER |
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Week of the Year
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A diamond worker has been contracting for 15 months with a diamond merchant. The merchant told him that he would be getting one diamond each month from a diamond chain with 15 diamonds . However, he can break only three links in the first month. He cannot break any more links after the first month. Which three links should he break up in order to be able to get one diamond each month?
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Break the link between second and third diamond, the link between third and fourth diamond and the link between seventh and eighth diamonds so that there will be 4 parts: one single diamond, 2 diamonds, 4 diamonds and 8 diamonds. He can take the single diamond at first month. He can get the double diamonds and give back the single diamond at second month. He can get the single diamond at third month. He can get the 4 diamonds and give back the single and the double diamonds and so on.
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Nine kiwis look identical except the one which is lighter. How can you weigh only 2 times on a balance scale to find out which one is lighter?
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If we give a number for each kiwi, say from 1 to 9. We put kiwi 1, 2, and 3 on the left and kiwi 4, 5 and 6 on the right and weight them. If they are balanced then we know kiwi 1 to 6 is OK. We just need to put kiwi 7 on one side and kiwi 8 on the other side and weight them. Now weighing them if one side is lighter, we get our lightest one. Otherwise, the one kiwi left aside will be lighter.
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If only 2 couples are existing today. Suppose each of these couple give birth to 4 children & the 8 children form 4 couples & each couple in turn give birth to 4 children, & those 16 form 8 couples & give birth to 4 children each & so on, can you tell exactly the number of persons existing after 10 generations, excluding the two initial couples?
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We start out with 2 couples, four people or 22 people who increase their progeny as follows: 23+24+25+26+27+28+29+210+211+212= 8184
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One morning at sunrise one hiker begins to walk up a hill on a narrow path that spirals around it from the bottom all the way up to the top. Of course, he walks with varying speed, taking breaks to rest and to eat his lunch. He reaches the top of the hill in the evening, spends the night in a tent, and then, in the morning, starts to walk back down along the same path. By the sunset he reaches the bottom of the hill. Note, that his speed on the way down is greater than his speed on the way up. Prove that there is a spot along the path that the hiker will occupy on both trips at precisely the same time of day.
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Imagine two people walking along the path toward each other at the same time (one from the top of the hill, the other one from the bottom). Obviously, they must meet somewhere along the way.
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In a grid of numbers, which will be greatest: the greatest of the smallest numbers in each column, or the smallest of the greatest numbers in each row?
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Smallest of the greatest will be greater than greatest of the smallest. Consider number X who is at the intersection of the column with the greatest of the smallest (G), and the row with the smallest of the greatest (S). Clearly, S ≥ X ≥ G (the equality will happen if the smallest of the greatest is the same number as the greatest of the smallest). Therefore, S > T.
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