### Brain Teasers

# 3-digit Numbers

There are four 3-digit natural numbers, each of them equals the sum of the cubes of its digits.

Three of them are:

153=1+125+27

370=27+343+0

407=64+0+343

Do you know what the fourth one is? It does not begin with 0, otherwise it isn't a 3-digit number.

Three of them are:

153=1+125+27

370=27+343+0

407=64+0+343

Do you know what the fourth one is? It does not begin with 0, otherwise it isn't a 3-digit number.

### Hint

It's much easier than it seems to be.### Answer

371.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

Nice one! I didn't get it but I should have because you gave us the 370 and it should have been obvious from there. Well constructed!

Sorry, not too good at math ..had to wrk with this for a while and then ask someone WHO I WILL mention........SO ANBARRAESED GREAT TEASER, KEEP THEM COMING. COULD USE A THING OR % LOLOL

I GOT IT .......I GOT IT. Keep them coming!!!!

Haha...wish I was good at math...lolol anyways great and awesome job. 2 thumbs up

I'm no good at math, but great teaser! Maybe when I get good at math I will do this one over again!

I don't know if this is a Teaser or not. I did not know where to begin. How?

I'm with you precious!! Not to mention that my math skills are not up to par.

Nice one Shenqiang.

If I'd had a couple of hours to work on it, I would have probably found the answer, but my brain isn't up to the task at the moment.

I GOT it was hard though i figured it out because of 370

Very nice! I thought it might be tedious, but I figured I could identify a relatively few number of candidates by working out the possible combinations to make the last digit. Each number from 0 to 9 cubed ends in a different digit.

For 0, 0^3 = 0, so the last digits of the other two cubes must add up to 10 so that 10+0 ends with a zero. For 1, 1^3 = 1, so the last digits of the other two cubes must add up to 10 so that 10+1 ends with a 1. As soon as I saw this relationship I realized that any number ending in zero could also end in one and the answer was obvious. Put a smile on my face!

For 0, 0^3 = 0, so the last digits of the other two cubes must add up to 10 so that 10+0 ends with a zero. For 1, 1^3 = 1, so the last digits of the other two cubes must add up to 10 so that 10+1 ends with a 1. As soon as I saw this relationship I realized that any number ending in zero could also end in one and the answer was obvious. Put a smile on my face!

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