What number?
I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
Age
5 to 7
Challenge level
Problem
Image
I am less than 25.
My ones digit is twice my tens digit.
My digits add up to an even number.
What am I?
Getting Started
You could look at one piece of information at a time. For example, which numbers are under 25?
Can you now look at another piece of the information and narrow down the options?
Student Solutions
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.
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.
Teachers' Resources
What Number?
Image
I am less than 25.
My ones digit is twice my tens digit.
My digits add up to an even number.
What am I?
Why do this problem?
This is a quick problem suitable for starting a lesson and requiring no resources. It can usefully be made into a longer activity by focussing discussion on the possible problem-solving strategies and evaluating them.
Possible approach
Offer the children time to work in pairs and record their thinking on large pieces of paper. Pin them up centrally and encourage the children to look for similarities and differences in the way the problem has been solved. Do they think one way is better than the others, and if so why?
You could make it a more structured discussion by writing the three pieces of information (less than $25$, ones double tens, add to even number) on three pieces of paper and ordering them differently, in each case writing down the possible numbers from the first piece of information and eliminating those that don't fit the second and the third. Do the children think one order was better than
the others?
Key questions
What do you know?
Can you make a list?
Possible extension
Children can make up similar questions for each other. Can they use three digits? Can they be sure there is only one answer to their question?
Possible support
Working in pairs to record thought processes can be very threatening for children who find such questions difficult. You could instead perhaps give them cards with numbers up to $25$ and they could remove the ones that didn't fit the other two conditions.