# Can Eight 8’s Produce 1000? My previous post “Can Two 2’s Produce 5?” showed a way to produce 5 using only two 2’s and any mathematical operations. Now, here’s another similar puzzle. Using eight 8’s and any mathematical operations and symbols, can you make them equal to 1000? There are several solutions.

## Solutions

When I asked this question to some of my friends, they were able to give me six basic solutions (though there are more): $888+88+8+8+8=1000$ $\frac{8+8}{8}(8\times 8\times 8-8)-8=1000$ $8(8\times 8+8\times 8)-8-8-8=1000$ $\frac{8888-888}{8}=1000$ $\frac{8888}{8.888}=1000$ (This solution has several variantions. Can you find them?) $8\left [8(8+8)-\frac{8+8+8}{8} \right ]=1000$

One of them was smart enough to use square roots and factorials, so he was able to find four more solutions: $\frac{8!}{8}-8\left [ (8\times 8\times 8)-8 \right ]-8=1000$ $8!\left [\frac{8+8}{8(88-8)} \right ]-8=1000$ $(8+8)(8\times 8)-(\sqrt{8+8})!+8-8=1000$ $\frac{8!}{8+8+8+8+8}-\sqrt{8}\times \sqrt{8}$

I have found more solutions which involve square roots and factorials. Can you find more?

This puzzle can be solved by producing 10³ using the 8’s: $\left (\frac{88-8}{8} \right )^{(8+8+8)/8}=10^3=1000$ $\left (8+\frac{8+8}{8} \right )^{(8+8+8)/8}=10^3=1000$

If special mathematical symbols are employed, more solutions can be found:

Floor and Ceiling Functions: $\left (\left \lfloor\sqrt{8} \right \rfloor+\left \lceil\sqrt{8} \right \rceil \right )\times\left (\left \lfloor\sqrt{8} \right \rfloor+\left \lceil\sqrt{8} \right \rceil \right )\times\left (\left \lfloor\sqrt{8} \right \rfloor+\left \lceil\sqrt{8} \right \rceil \right )\times \sqrt{8}\times \sqrt{8}=1000$

Base 8 logarithm: $(\log_{8}8\times 8)(8\times8\times8-8)-8=1000$

Binomial Coefficient: $\left [\binom{8+8}{\frac{8}{.8}}-8 \right ]\div 8+8-8=1000$

Gamma Function: $\frac{8\Gamma (8)}{8+8+8+8+8}-8=1000$ $\Gamma (8)-(8\times 8)\left (8\times 8-\frac{8}{8} \right )-8=1000$

Finally, this solution involves base 8 numbers: $\left (\frac{88}{88}\times 8\times 8\times 8 \right )_8=1000_8$

However, this is not an acceptable solution since the answer is in base 8 and 1000 in base 8 is equal to 512 in base 10. Any interested reader may try to find a valid solution using base 8 numbers. ### Posted by Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

## 16 thoughts on “Can Eight 8’s Produce 1000?”

1. Smitha V says:

This is so interesting. Am going to share it with my daughter who loves Maths. Thanks for the post. Got me thinking.

Liked by 1 person

1. Edmark M. Law says:

Thanks.

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2. printz007 says:

888+88+8+8+8 = 1000

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3. jfrels says:

Also 1000 in binary = 8 decimal

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4. jfrels says:

Do square roots count as that as an exponent of 0.5?

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5. Johnny Spangles the Haemorrhoid says:

I have £8 left in my bank account, if you could make that into £1000 I’d be much obliged.

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1. Edmark M. Law says:

I could do that, though who knows how long it would take.

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6. sunnydaysinseattle says:

Nicely done!

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7. Patchious patch says:

WOw ! .. by the way thanks for stopping by my blog :)

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8. superwifeandmummy says:

You won’t believe me when I say, my next poem I’m publishing this week is about Maths. Unfortunately, I don’t think I quite share your love and fascination of it. .but fab post!

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1. Edmark M. Law says:

I look forward to reading it :)

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9. microadventuresmap says:

((8×8)+(8×8))x8-8-8-8=1000 😀

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1. Edmark M. Law says:

Correct :)

Though it’s already been listed.

Thanks for participating :)

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10. Garfield Hug says:

🤔My mind has been blown🙈

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11. hollythreesixfive says:

Good grief! I can do that many computations. I can draw the 8 or write a poem about the 8, but I’ll never find a solution to the 8’s math puzzle. Except maybe MAYBE I could have come up with the first solution if I had really tried and didn’t mind smoke coming out of my ears.

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1. Edmark M. Law says:

There is a couple of easy solutions. I’m sure that you’d be able to find them. The other solutions are quite hard though…

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