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?
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
Zachary, Stephen and Natasha who are all
pupils at Trinity Middle School in Newport, Isle of Wight sent us
correct answers to this problem.Stephen said:
I decided that if you don't use a 9 last in the 4 numbers at the
top it would work out.
Yes - we agree Stephen, it is the third digit
in the 4-figure number which is the sum of consecutive numbers.
Natasha looked up the clues. She wrote the
numbers on pieces of card and then jiggled them about.
Kirsty from St Aldhelms School in Poole agreed
that it must be the third digit of the 4-digit number which is the
sum of consecutive numbers. She explained very clearly how she
arrived at her answer:
The only three consecutive numbers that can go in the 4-figure
number are 4, 5 and 6. 7, 8 and 9 are too big. The sum of any two
of these is greater than 9. For example:
7 + 8 = 15
8 + 9 =17
9 + 7 = 16
0, 1 and 2 cannot go on the first line because:
0 x 3 = 0 (same number twice)
1 x 3 = 3 (same number twice)
Therefore the third number must be 9 (5 + 4) beause 6 + 5 and 6 + 4
are both too big.
The fourth number in the 4-figure number cannot be 5 as 5 x 3 = 15
(repeat digit 5).
The fourth number also cannot be 6 as then we would get 8 twice, so
it must be 4.
So, the last two digits must be 5 then 6 so they're not in
This is the answer all four agreed on:
Well done, particularly to Kirsty for her