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# Make Three 7's equal 10

## Question

You want to satisfy

7 7 7 = 10

You can add, subtract, multiply and divide, use parentheses, square root, exponent and factorial. So, for example:
2^2 + 2^2 +2 = 10
Sqrt(4) + 4 + 4 = 10

8 + 8^0 + 8^0 = 10

You are also not allowed to manipulate the right side of the equation (e.g. 7^0 * 7^0 * 7^0 = 10^0).

## Recommended Posts

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57 minutes ago, Heureka said:

You can add, subtract, multiply and divide, use parentheses, square root, exponent and factorial.

Using the number 0 or extra 2's does not fit the allowed operations.

Only Sqrt(4) + 4 + 4 = 10 seems allowable.

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4 hours ago, bonanova said:

Using the number 0 or extra 2's does not fit the allowed operations.

Only Sqrt(4) + 4 + 4 = 10 seems allowable.

Rats, I was going to say that ( Sqrt(7!) - 7^0 ) / 7 is close enough that no one's likely to notice the difference.

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Posted (edited)
On 8/25/2021 at 3:39 PM, bonanova said:

Using the number 0 or extra 2's does not fit the allowed operations.

Only Sqrt(4) + 4 + 4 = 10 seems allowable.

I don't see anything barring use of other numbers in exponents. Nothing explicitly says you can only use 7s. It's certainly implied that the 3 7s are the central parts so you can't do something like add or subtract a different number but you can square or cube.

Closest I can get with the more limited interpretation: 7!/sqrt(7!)÷7=10.14

Looser interpretation: (7!)^(1/5)+(7!)^(1/5)-7^0=10.003

Edited by Thalia
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Posted (edited)
Spoiler
On 8/26/2021 at 5:24 AM, plasmid said:

Rats, I was going to say that ( Sqrt(7!) - 7^0 ) / 7 is close enough that no one's likely to notice the difference.

Just add "ceiling" in front of your equation to get exactly 10!

Edited by rocdocmac
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Spoiler

Using 3x 7 and 1x 0 only(follow-up on my comment to plasmid)

Spoiler

Rather use flooring! In Excel it will look something like this ... =FLOOR((SQRT(FACT(7)))/7,(7^0))

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