IF THREE CATS catch three rats in three minutes, how many cats will catch 100 rats in 100 minutes?
SOLUTION
The usual answer to this old riddle is as follows. If it takes three cats three minutes to catch three rats, it must take them one minute to catch one rat. And if it takes them a minute for each rat, then the same 3 cats would catch 100 mice in 100 minutes. Unfortunately, it is not quite that simple; such an answer presupposes something that is certainly not stated in the problem. It assumes that all three cats concentrate their attention on the same rat until they catch him in one minute, then turn their combined attention toward another rat. But suppose that instead of doing this, each cat chases a different rat and takes three minutes to catch it. In this case, three cats would still catch three rats in three minutes. It would take them siX minutes to catch six rats, nine minutes to catch nine rats, and 99 minutes to catch 99 rats. A curious difficulty now faces us. How long will it take those same three cats to catch the 100th rat? If it still takes them the full 3 minutes to run him down, then it will take 3 cats 102 minutes to catch 100 rats. To catch 100 mice in 100 minutes-assuming this is how the cats go about their mice catching-we will certainly need more than 3 cats and less than 4 cats. Of course, it is possible that when the three cats gang up on a single rat they can cover him in less than three minutes, but there is nothing in the statement of the riddle that tells us exactly how to measure the time for this operation. The only correct answer to the problem, therefore, is this: The question is ambiguous and cannot be answered without more information about how those cats catch rats.
MRS. PU FFEM 'S CIGARETTES
MRS. PUFFEM, a heavy smoker for many years, finally decided to stop smoking altogether. "I'll finish the twenty-seven cigarettes I have left," she said to herself, "and never smoke another one." It was Mrs. Puffem's practice to smoke exactly two-thirds of each cigarette. It did not take her long to discover that with the aid of some cellophane tape she could stick three butts together to make a new cigarette. With 27 cigarettes on hand, how many cigarettes can she smoke before she gives up the weed forever?
SOLUTION
After smoking the 27 cigarettes, Mrs. Puffem patched together the butts to make 9 more. These 9 cigarettes left enough butts for 3 more clouds of smoke; then with the 3 final butts, she made one final Cigarette. Total: 40 cigarettes. Mrs. Puffem never smoked again; she failed to recover from the strength of her final puff.
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