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