Puzzles
15 December
The arithmetic mean of a set of \(n\) numbers is computed by adding up all the numbers, then
dividing the result by \(n\).
The geometric mean of a set of \(n\) numbers is computed by multiplying all the numbers together, then
taking the \(n\)th root of the result.
The arithmetic mean of the digits of the number 132 is \(\tfrac13(1+3+2)=2\).
The geometric mean of the digits of the number 139 is \(\sqrt[3]{1\times3\times9}\)=3.
What is the smallest three-digit number whose first digit is 4 and for which the arithmetic and geometric means of its digits are both non-zero integers?
16 December
Arrange the digits 1-9 in a 3×3 square so that:
the median number in the first row is 6;
the median number in the second row is 3;
the mean of the numbers in the third row is 4;
the mean of the numbers in the second column is 7;
the range of the numbers in the third column is 2,
The 3-digit number in the first column is today's number.
| median 6 | |||
| median 3 | |||
| mean 4 | |||
| today's number | mean 7 | range 2 |
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.