Square and Even

Arrange the numbers on the squares so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even.

How many different ways can this puzzle be solved using these digits?

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A Mathematics Lesson Starter Of The Day


Topics: Starter | Number | Problem Solving

  • K. Rybarczyk, Knightswood Secondary
  • With younger pupils, it is a good idea to begin with a reminder about square numbers. Also some practice with squares and square roots on a calculator.
    Next, give a simplified 4 digit version of the same problem. The digits 1, 4, 6, 8 work well.
    Now give the 9 digit version as in this starter.

    [Transum: Excellent idea KR. Here is the simplified version that you suggested.]
  • Ole And Daisy, Beckley School
  • We love this website and we love this starter. It was very challenging and fun.
  • Michael Guthrie, Drumkeen, Co Donegal
  • There is another way of doing this
    144 12 squared
    256 16 squared
    484 22 squared.
  • KentuckyJohn, Ramen School
  • Very good game.
  • Transum,
  • One way to solve this problem using technology is to use a spreadsheet or a graphic display calculator to generate a list of all 22 three digit square numbers. Manually eliminate those that contain a 0, 3, 7 or 9 as those digits aren’t available. Only one of the 8 square numbers left is comprised of only even digits so this number must go in the bottom row of the grid. Eliminate square numbers from the list that can not be made using the remaining six digits. It is now quite easy to find all of the possibilities. Teachers, tutors and parents can see all of the possible answers below.

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This starter has scored a mean of 3.1 out of 5 based on 691 votes.

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Here are all of the possible answers:

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Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.


Here is the URL which will take them to a game involving square numbers.


Student Activity


Too difficult? Try the simplified version (two digit numbers).


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