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Solve the L-puzzle

By David Shaw, 31 January 2017

Can you solve this tricky puzzle?

Here are two tricky puzzles, which look strangely similar. Did we somehow get a puzzle inside your puzzle?

You will need

• Scissors
• Copy of the printouts, which you can download here (two pages)

What to do

1. Cut out four of the small L‑shapes and the smaller L‑shaped grid.
2. First challenge! Fit the four small L‑shapes into the L‑shaped grid. They should cover every square in the grid. Need a hint? Scroll down to the pictures.
3. Cut out the remaining 12 small L‑shapes and the larger L‑shaped grid.
4. Time for a bigger challenge! Use all 16 small L‑shapes to cover the larger L‑shaped grid. This is even harder than the first challenge. Stumped? Scroll down to the pictures for a hint.

Click for a hint to the first challenge

Click for the answer to the first challenge

Click for a hint to the second challenge

Click for the answer to the second challenge

What’s happening?

At first glance, the second, larger puzzle seems much harder than the first. That is, unless you realise that you can use the answer to the first puzzle to solve the second.

In the first puzzle, you make a medium sized L‑shape out of four smaller L‑shapes. In the second puzzle, you make a larger L‑shape out of 16 small L‑shapes. The trick is to add a step in the middle. You have enough small L‑shapes to make four medium sized L‑shapes. Suddenly, the puzzle is just a bigger version of the first.

This mind-bending property, where something is made from itself, is called recursion. It is very useful in computer programming. Many computer programs also have recursive jokes in them. For example, if you search for recursion on Google, it will suggest you instead search for recursion!

There are also non-recursive answers to this puzzle. If you have some time, see if you can find one.

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