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 3.1 out of 5 based on 681 votes.

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



Here are all of the possible answers:

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.


Texas Instruments Nspire Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Click the images above to see all the details of these items and to buy them online.

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).


©1997-2020 WWW.TRANSUM.ORG