Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
An odd version of tic tac toe
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Thank you for all the solutions you sent
to this problem. Akash from South Island School used clear
reasoning to reach an answer:
If the number's digits add up to an even number, then the digits
will be either odd &
odd or even & even.
If the ones digit is twice as much as the tens digit, then both
the digits must be even. This is because of the fact that if an odd
digit is multiplied by $2$, the product is always even.
Till now: Solution has even & even digits. The number is
smaller than $25$. This means that the first digit has to be $2$.
If the first digit is $2$, $2\times2=4$.
So the answer is $24$.
By the way, the number could be $00$ as well if it is
and Syed from Foxford School and
Community College, both used the same method. Syed says:
To solve this problem I go through one clue at a time and use my
elimination skill to find out what the number is:
Clue 1 : 'I am less than $25$'
So from this clue I list all the numbers below $25$.
$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24$
Clue 2 : 'My unit digit is twice my tens digit'
This clue can be split into smaller clues:
'It has a tens and unit digit'
So now I get rid of all the numbers from the list from clue 1 that
don't apply to this clue. So I have:
$10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24$
'Its unit digit is twice its tens digit'
Clue 3: 'My digits add up to an even number'
$1 + 2 = 3$ which not an even number so that it can only be:
Alexis approached the problem slightly
differently. He wrote:
Many of you used Alexis' method, including
Alex and Phoebe from Newton Poppleford Primary. Finally, Michaela
from St Michael's C of E Primary had another way of solving the
But why did you only write down the even
numbers to start with, Michaela? How did you know the answer was
Well done all of you for explaining your
reasoning so clearly.