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