# Number Detective

Follow the clues to find the mystery number.

## Problem

*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.

- 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.

## Getting Started

Which clue will you use first?

Is there some way you could sort the numbers that would help?

## Student Solutions

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

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.

Shivoham from Robin Hood Junior School also sent in a picture showing the working out.

From Westridge School for Girls in the USA these three Sandhya, Salvia and Saba sent in good solutions.

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.

## Teachers' Resources

**Why do this problem?**

### Possible approach

### Key questions

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.