### Brain Teasers

# Eighth Powers

There are three 8-digit natural numbers, each of them equals the sum of the eighth powers of its digits.

Two of them are:

24678050=256+65536+1679616+5764801+16777216+0+390625+0

88593477=16777216+16777216+390625+43046721+6561+65536+5764801+5764801

Do you know what the remaining one is? It does not begin with 0, otherwise it isn't an 8-digit number.

Two of them are:

24678050=256+65536+1679616+5764801+16777216+0+390625+0

88593477=16777216+16777216+390625+43046721+6561+65536+5764801+5764801

Do you know what the remaining one is? It does not begin with 0, otherwise it isn't an 8-digit number.

### Hint

It is between 24678050 and 88593477.### Answer

24678051.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

yay, im the first one! Oh yeah, I dont like math, but good job

its so unbelievably simple!

how do you expect us to solve this teaser? its either you know the answer(maybe read it somewhere) or you dont. this teaser dont have any solution.

Nice teaser!

To pating: the teaser has a simply deduced solution by applying a logic and a small amount of math knowledge. Seeing that one of the given numbers ends with a zero, the fact that 1^8 - 0^8 = 1 means that replacing the zero with a one must produce the missing value.

I'll admit that I probably wouldn't have found that if I hadn't applied the reasoning that the teaser couldn't expect us to find the answer by a brute force search. Given that assumption I reasoned that the missing number was somehow related to one of the provided numbers and then saw the answer.

To pating: the teaser has a simply deduced solution by applying a logic and a small amount of math knowledge. Seeing that one of the given numbers ends with a zero, the fact that 1^8 - 0^8 = 1 means that replacing the zero with a one must produce the missing value.

I'll admit that I probably wouldn't have found that if I hadn't applied the reasoning that the teaser couldn't expect us to find the answer by a brute force search. Given that assumption I reasoned that the missing number was somehow related to one of the provided numbers and then saw the answer.

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