Police Line Up

Task 119 ... Years 2 - 8


A language and logic puzzle that opens the door to a wealth of cross-curriculum activity. The focus is on mathematical reasoning and the task offers stimulating cartoon characters to grab student interest. Clues are provided allowing the students to sort the characters into order by height.

This cameo has a From The Classroom section which has examples of Police Line Up puzzles created by students.



  • 10 character cards


  • mathematical language related to space and order
  • spatial facts and relationships
  • problem solving strategies
  • number facts and relationships
  • combination theory
Police Line Up


A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

Students will need to interpret some aspects of the language as they work through the clues. For example, will they interpret 'somewhere between' to mean anywhere between and the clue 'between' to mean exactly between. There is also choice in the clue 'next to'- left or right of the named person? These variations in the meaning of language lead to two possible orders (at least):

Solution 1
Bugsy, Frankie, Clyde, Bert, Fingers, Benny, Spike, Lefty, Mike, Mugsy

Solution 2
Bugsy, Frankie, Clyde, Bert, Spike, Lefty, Mike, Fingers, Benny, Mugsy

and in either case the fourth tallest suspect is Bert.

That fact that there are two known solutions demands that we ask the mathematician's questions:

  • How many solutions are there?
  • How do we know we have found them all?

If however the word between in:

Frankie is standing between Bugsy and Clyde.
is also taken to mean somewhere between, then the line up changes and the answer would be Clyde.

An obvious extension to the puzzle comes from wondering about how it was constructed in the first place. Students readily see that someone must have arranged the line first and then decided the clues that allow one character to be identified. The challenge now is for students to create their own puzzle, however it is a good idea to start with fewer, say four, characters. This challenge is likely to be even more absorbing for the students if they can first create their own characters.

Another extension, which introduces a wealth of number work, comes about by suggesting that, at least in comic strips, criminals are given numbered uniforms. Provide the students with a sticky-note pad and ask them to assign a number to each character:

...that shows me as much as you can about what you know about numbers.
Clues are now developed based on the number assigned to each character. See examples in From The Classroom below.

Older secondary students could be encouraged to explore the combination theory associated with lining up the characters. If there are no clues, there are 10! arrangements. However, a clue such as 'Benny is next to Bert' reduces this number to 2 x 9! Choose another clue. How does this affect the number of possibilities? However, using 10 characters makes this quite a complex exercise, so probably better to first design a puzzle with four or five characters.

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

There are several ways to introduce Police Line Up as a whole class investigation, but perhaps the most exciting is to sketch (or enlarge) ten character cards and ask ten volunteers to hold them. The clues can be written out as one set that all other pairs receive (remember, you are not allowed to photocopy the card), or as one clue per strip of paper. In this second approach each pair not in the line up is in charge of one clue - they are Clue Pairs. In a kind of well managed chaos, Clue Pairs instruct line up people in a way that satisfies their clue, but also takes account of the demands of other Clue Pairs.

Explore the problem as outlined above, highlighting aspects of the Working Mathematically Process as part of the investigation.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 46, Police Line Up, which includes several alternative clue sets.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Police Line Up task is an integral part of:

  • MWA Space & Logic Years 3 & 4

The Police Line Up lesson is an integral part of:

  • MWA Space & Logic Years 3 & 4
  • MWA Space & Logic Years 7 & 8

Police Line Up task is also included in the Primary Library Kit. Solutions for tasks in the latter kit can be found here.

From The Classroom

Mayfield Primary School

Mrs. Stagg
Year 5/6
Children in Mrs. Stagg's class created their own line up puzzles.
Solutions are at the bottom of the page.

Crime Line Up
  1. Half of 14 is next to 3 less than 12.
  2. The two digits that add up to ten, and the number 7 have four numbers between them.
  3. The 3 digits that add up to two are next to the 2 digits that add up to ten.
  4. The 2 digits that make 72 if you times them are next to the number which is 3 less than twelve.
  5. The two digits that add up to three are in between the 2 digits that make 72 if you times them and the three digits that add up to 2.

People Line Up
  1. The two digits that add up to 6 are first in line.
  2. The two digits that become two if you times them are next to the number 2.
  3. The two digits that add up to 9 are in between 60 and 2.
  4. The two digits that add up to 7 and are one less than 44 are next to 61 which is last in line.


In each case, there may be more than one answer.

Green Line
Follow this link to Task Centre Home page.