Gram Electronic
Saturday, February 27th, 2010Gram Electronic
A couple of riddles I need to know answers for.?
1. A student is given 5 random cards from a standard deck of 52 cards. He
must choose 4 cards to reveal to his professor and the order in which to
reveal them; his goal is to reveal four cards in such a way that the
professor knows what the fifth hidden card is. How does he do this?
2. You have ten cans of peas. The cans are open. In each can, there are 100 peas. In 9 of the ten cans, each pea weighs 1 gram. In the tenth can, each pea weighs only .9 grams. You do not know which can has the smaller peas, nor is it possible to tell with the naked eye. To help you, you have an Electronic Scale. However, the scale is not in great shape, and can only provide one correct measurement before permanently malfunctioning. How can one, using only the one measurement afforded by the scale, determine beyond a shadow of a doubt which can it is that has the smaller peas?
On the scale all together, put 1 pea from the first can, 2 peas from the second can, 3 peas from the 3rd can, and so on, up to 10 peas from the tenth can. If each pea weighed 1 gram, you would have 55 grams. Since some of the peas weigh only .9 grams, you will be anywhere from 1 tenth to 10 tenths (1 whole gram) short of 55 grams. However many tenths you are short, this is the can the smaller peas are in.
For example, if all the peas together weigh 54.6 grams, then there are 4 tenths missing from 55 and 4 peas that weigh .9 grams. Since you put 4 peas on the scale from the 4th can, you know the 4th can has the smaller peas.
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