Number Detective
Follow the clues to find the mystery number.
Age
5 to 11
Challenge level
Number Detective printable sheet
Calling all detectives!
You will need to think creatively, use your reasoning skills and your problem-solving strategies to find the mystery number from the table below.
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- The number has two digits.
- Both of the digits are even.
- The digit in the tens place is greater than the digit in the ones place.
- The ones digit is not in the three times table.
- The tens digit is not double the ones digit.
- The sum of the two digits is a multiple of five.
|
18 |
86 |
|
120 |
42 |
|
46 |
64 |
|
80 |
8 |
|
22 |
83 |
You might now like to play the game Statement Snap or have a go at Satisfying Four Statements.
Which clue will you use first?
Is there some way you could sort the numbers that would help?
We had over 100 new submissions for this popular challenge. First from Orchards School in Wisbech, Cedar Class
Amelia says, “8 and 120 are not the number because 8 is one digit and 120 has 3 digits.”
Aironas then adds, “It can't be 18 or 83 because they have odd digits.”
“46 and 22 don't have a tens number greater than the units number, so it can't be them,” suggests Matas.
Jessica states, “86 is not it because it has 6 in it (the 3x) and the rest are not.”
Tommy D says, “It isn't 42 because the tens digit is double the ones digit.”
There are now only 2 possible answers left: 64 and 80.
Lastly, Tommy C goes for it! “I think 64 is the answer because 6 + 4 = 10 and 10 is in the 5 times table.”
Cedar Class have also made their own Number Detective challenges!
You are welcome to try them”¦Their document can be viewed hereCedar Class Wisbech.docx
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From the same school but from Hawthorn Class (Year 3), Colleen sent in the following:
The answer is 64 as we worked it out by using the steps and crossing off any answers which didn't meet the criteria.
The answer is not:
• 120 and 8 as they do not have two digits. 120 have three digits and 8 has one digit.
• 83 and 18 did not have two even numbers
• In 22 tens and units are equal. In 46 the ones are greater than the tens.
• In 86 the 6 is a multiple of 3
• In 42 double the 2 is 4
• In 80 the sum of the digits is 8 which is not a multiple of 5
Isabel from Clyst Heath Primary School sent in the following:
I read the clues first and decided to start with the last clue because that would eliminate most of the numbers - The sum of the two digits is a multiple of 5. That left me with 64/46. Then I searched for a clue that would allow me to cancel out one without easily. I chose the clue, The tens digit is bigger than the units digit, that allowed me to cancel out 46
leaving me with 64 and thats my answer.
Jacob from St. John's Primary sent in a picture of his work.
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Shivoham from Robin Hood Junior School also sent in a picture showing the working out.
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From Westridge School for Girls in the USA these three Sandhya, Salvia and Saba sent in good solutions.
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I recommend that you view larger versions here.
Sandhya.JPG
Salvia.JPG
Saba.JPG
Thank you all so much for these excellent solutions and sharing how you found the answer.
Number Detective
Number Detective printable sheet
Calling all detectives!
You will need to think creatively, use your reasoning skills and your problem-solving strategies to find the mystery number from the table below.
Image
- The number has two digits.
- Both of the digits are even.
- The digit in the tens place is greater that the digit in the ones place.
- The ones digit is not in the three times table.
- The tens digit is not double the ones digit.
- The sum of the two digits is a multiple of five.
|
18 |
86 |
|
120 |
42 |
|
46 |
64 |
|
80 |
8 |
|
22 |
83 |
You might now like to play the game Statement Snap or have a go at Satisfying Four Statements.
Why do this problem?
This is a curious problem that taps into children's fascination to solve mysteries. It offers opportunities to reinforce the language and characteristics of numbers such as odd, even, multiple. However it is also a problem which can be tackled in a systematic way, or, more elegantly, through insightful reading of the clues. Comparing
the two methods can be a useful exercise in considering what mathematical thinking looks like and shows children that there is more than one way to solve a problem.
Possible approach
Put three two-digit numbers, such as 93, 56, 75 on the board and ask the children which is the odd one out and why. Listen for explanations which include descriptions of place value, odds and evens, and perhaps multiples.
Say that you are going to choose one of them secretly and they can ask just one or two questions to see if they can find which one it is. For each correct guess ask the children to justify their answer. Are they curious to know if they are correct?
Put 23, 45, 62, 101, 94 on the board and tell then you have chosen one of these. What questions would be good ones to ask and why? Make a record of the questions on the board so that the children can refer to them. Again, ask the children to justify any conclusions they come to.
Then offer the problem to pairs of children. Say that you are interested in the mystery number but also how they know and you will be asking for a description of what they did and in what order, so they may like to keep some notes.
Bring the children back together and ask a few pairs to describe their method. Listen for those who go through the clues in order eliminating the impossible numbers, and explain that working systematically is a very important skill for a mathematician. Notice how children persevere to keep going.
But also look out for the children who have scanned through the clues to find one that is more useful and saves some work - for example:
'The sum of the two digits is a multiple of five which means the magic number must be 46 or 64.'
After that we only need one more carefully chosen clue to distinguish between them:
'The digit in the tens place is greater than the digit in the unit (or ones) place.'
Discuss the importance of scanning through to see which clues might be the most useful.
Key questions
Which question shall we ask first? Why?
What does 'multiple of five' mean?
Which clue/s were you curious about first?
Which clue/s were you curious about first?
Possible extension
An obvious extension is for the children to make up their own examples for each other. They could repeat the format of the given problem, or play 'what's my number?' with a partner, where they try to find out what the mystery number is in the minimum number of guesses. Give an opportunity for them to describe why some questions are more useful than others.
Possible support
Sometimes it can be confusing to be given too much information at one time. Write the clues and the numbers out on separate cards. Spread the number cards out and offer the clues one at a time, encouraging discussion of the characteristics of each number in response to the clue.