Difficult Riddles

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How many cats are in a small room if in each of the four corners a cat is sitting, and opposite each cat there sit three cats, and a each cat’s tail another is sitting?
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When the celebrated German mathematician Karl Friedrich Gauss (1777-1855) was nine he was asked to add all the integers from 1 through 100. He quickly added 1 to 100, 2 to 99, and so on for 50 pairs of numbers each adding to 101. Answer: 50 X 101=5,050. What is the sum of all the digits in integers from 1 through 1,000,000,000? (That’s all the digits in all the numbers, not all the numbers themselves.)
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Draw four rectangles on a piece of paper. Put nine x’s in the four rectangles so that there is an uneven number of x’s in each rectangle.
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An alarm clock runs 4 minutes slow every hour. It was set right 3 1/2 hours ago. Now another clock which is correct shows noon. In how many minutes, to the nearest minutes, to the nearest minute, will the alarm clock show noon?
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Many-manned scud-thumper, Maker of worn wood, Shrub-ruster, Sky-mocker, Rave! Portly pusher, Wind-slave. What am I?
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You have accidently left out the plug and are attempting to fill the bath with both taps full on. The hot tap takes 6 minutes to fill the bath. The cold tap takes 2 minutes and the water empties through the plug hole in 4 minutes. In how many minutes will the bath be filled?
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