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?

Your answer is not correct.

Press the Clear button and try again.

The numbers in the circles can be moved by dragging them using a mouse or your finger (if you have a touch screen or interactive whiteboard).










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.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.2 out of 5 based on 261 votes.

Previous Day | This starter is for 10 February | Next Day



Here are all of the possible answers:

Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

Online Maths Shop

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).


©1997-2017 WWW.TRANSUM.ORG