### Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

### Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

### Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

# Base Puzzle

##### Stage: 3 Challenge Level:

1000, ?, 100, 31, 24, 22, 20, 17, 16, 15, 14, 13, 12, 11, 10

The solution to this problem is that all the numbers are the decimal number 16 in bases ranging from base 2 (binary) to base 16 (hexadecimal).

The first number, 10000, is in base 2, corresponding to 16 in decimal or base ten: with components one 16 and no 8's, 4's, 2's or 1's,

Therefore the second number should be in base 3, with components one 9, two 3's and one unit. The missing number is 121.

Solutions were received from Alex Skilton, age 15, The King's School, Canterbury, UK, Soh Yong Sheng, and Ling Xiang Ning of Raffles Institution, Singapore, and David Lowe, age 15, Trinity School, Carlisle, UK.