### Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

### Number Detective

Follow the clues to find the mystery number.

### Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

# What Number?

##### Age 5 to 7 ShortChallenge Level
We had just a few correct solutions and these ones came from from Pakuranga Heights Primary School in New Zealand. First Blaize and Abhishek and then one from Grace.

Blaize, 1+1=2
Abhishek, 12+12=24

Grace, if the number is under 25 and it adds up to an even number, but the ones digit is twice the tens digit then when you get it, it will be easier. Here is a clue I'm giving you. The ones digit is 4, so what is half of four and then you'll get your answer.

Katarina, 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'
12, 24

Clue 3: 'My digits add up to an even number'
1 + 2 = 3 which not an even number so that it can only be 24

Alexis approached the problem slightly differently writing:

Since the ones digit has to be twice the tens, I made a list of those possible numbers: 12, 24, 36, 48  ...
But it has to be less than 25: 12 and 24
Adding the digits has to result in an even number: 1+2=3, 2+4=6
6 is an even number so 24 is the answer!

Thank you for all these contributions and explanations to show your thinking.