Head and Feet like a Cat

I have a head like a cat and feet like a cat, but I am not a cat. What am I?




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One is to three as three is to five and five is to four and four is the magic number.
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Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

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A clock loses 10 minutes each hour. If the clock is set correctly at noon, what time is it when it reads 3 PM?

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Find the missing number in the sequence.

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There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

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