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?
Follow the clues to find the mystery number.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There were seven solutions to this alphanumeric, and four people
or groups found all seven: Andrei (School 205, Bucharest, Romania),
Sim (Raffles Girls' Primary, Singapore), Prateek (Riccarton High
School, New Zealand) and Damen, Katrina and Oliver (Crownfield
Junior School, England). A number of pupils from Crownfield Junior
School produced good work on this problem.
The key to this sort of problem is to be systematic, and Andrei
explained very clearly how he worked through every possibility.
Here is his solution:
I started from the observation that I must add two 3-digit
numbers, and the result is 4-digit one, so that I must assign the
value 1 to the letter F.
My method is to give values to the letters from right to left,
the way additions are performed. [O is also a good place to
start as it occurs three times. - Ed.]
So, the only solutions are: