# Blog

## Broken calculator

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Imagine your calculator is broken. Although it will still display numbers, only the 4 key, + key, = key and clear key work.

Starting at 0, can you get the calculator to display 1000? What’s the fastest way, with the fewest button presses?

It’s definitely possible to get this calculator to display 1000. You could press 4 + 4 + 4 + … and after 250 fours, you’ll get the right answer. But there are also faster ways.

If you start with 44 or 444, you’ll get to your goal much faster. The best solution combines both of these numbers. Using 444 is the most efficient way to make big numbers with few button presses, so it’s a good place to start.

444 + 444 = 888 is most of the way there. You can’t add another 444 without going over the goal, so instead, add some 44s.

444 + 444 + 44 + 44 = 976, and then add more 4s to finish it off:
444 + 444 + 44 + 44 + 4 + 4 + 4 + 4 + 4 + 4 = 1000

This solution takes just 26 button presses all up!

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## 4 responses

1. David

Actually, depending on how your calculator works, you might be able to get it even faster! what’s your best score?

2. Martin

I managed to do it in 20 presses
4+=+=+4=+====+=+====
this works out as
4, 8, 16, 20, 40, 60, 80, 100, 200, 400, 600, 800, 1000

a slightly different way, but still 20 presses
4+=+=+4=+=+====+====
works out as
4, 8, 16, 20, 40, 80, 120, 160, 200, 400, 600, 800, 1000

these work of the windows calculator, but not on my Casio fx-350c since “4+=” just gives “4”

3. Jyagaimasu

On my calculator I can only do it in 22 as 4+= will syntax error.
444+444+44+44=+4======.

4. Daniel Jeffers

Cool Equation

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