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Puzzles

4 December

The geometric mean of a set of n numbers is computed by mulitplying all the numbers together, then taking the nth root.
The factors of 9 are 1, 3, and 9. The geometric mean of these factors is
$$\sqrt[3]{1\times3\times9}=\sqrt[3]{27}=3$$
What is the smallest number where the geometric mean of its factors is 13?

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22 December

22 is two times an odd number. Today's number is the mean of all the answers on days (including today) that are two times an odd number.
Clarification: You are taking the mean for answers on days that are two times an odd numbers; ie. the days are two times odd, not the answers.

21 December

Today's number is a multiple of three. The average (mean) of all the answers that are multiples of three is a multiple of 193.
Tags: averages, mean

16 December

Today's number is four thirds of the average (mean) of the answers for 13th, 14th, 15th and 16th December.

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Mean, median, mode, range

A Find five one-digit positive integers which have a mean of 4, mode of 6, median of 4 and a range of 5.
B Find five one-digit positive integers which have a mean of 3, mode of 1, median of 1 and a range of 8.
C Find five one-digit positive integers which have a mean of 3, mode of 2, median of 2 and a range of 5.

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