Without Lifting The Pencil

By clicking the dots on the diagram to the right can you show how it can be drawn by going over each line once and only once?

Some of the diagrams it is possible while others it is not.

You can earn a trophy for indicating which diagrams are impossible and by tracing the route that completes the others.

Click on the tabs above to switch between the diagrams then click the 'check' button below when you have finished.

Check Start Again

I am convinced this shape is impossible.

I am convinced this shape is impossible.

I am convinced this shape is impossible.

I am convinced this shape is impossible.

I am convinced this shape is impossible.

I am convinced this shape is impossible.


This is a computer version of the classic pencil and paper puzzles in which the objective is to trace the diagram without taking the pencil off the paper and without going over the same line twice.

In this version you are required to click on the dots to show the route of the pencil. The 'Start Again' button is provided to let you erase incorrect attempts.

At least one of the diagrams is impossible to draw in this way. A tick box is provided below the diagrams for you to indicate the impossible diagrams.

When you think you have traced all of the diagrams you can and ticked the tick box of the others you can click on the check button to see if you are right. When you have all six diagrams correct you can collect a Transum Trophy for your efforts.

There is printable worksheet to go with this activity and also an activity called Bridge Crossings based on similar principles.

The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

Bill Brown,

Friday, May 31, 2019

"I've been toying with the house with an X drawing and trying to mathematically figure out the number of possible correct solutions.

I believe I am on the right path but lack the education to go further. So I begin 8 lines to be drawn with 5 possible starting points, depending on which vertex is selected as the starting point there are 2, 3 or 4 choices for the first line. 2 at the apex of the roof, 4 at each top corner and 3 at each bottom corner. The second line reduces each vertex choice by 1 since you can't redraw the first line. As far as I can trial it, this "choice rule" holds until the 5th line. At this point you have returned to a previously visited vertex. Here I see the "choice rule" changes to # of 2nd line degrees for that vertex minus # of previous visit until 0 choices remain and success if you have 8 lines. Less than 8 lines and it fails.

My problem is how to convert these observations into a number of possible successful solutions? "

Puzzle Lover,

Saturday, September 21, 2019

"The puzzles were easy once you solve the first one, the rest need barely any effort at all! I love puzzles like this!"

Hayden, Canada

Tuesday, February 14, 2023

"Fun, simple, and enjoyable. if I had a complaint i'd like them to become more challenging by the end."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


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