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3-digit Numbers

Math brain teasers require computations to solve.


Puzzle ID:#27426
Fun:*** (2.75)
Difficulty:*** (2.55)
Submitted By:shenqiangAcn****!!




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

Three of them are:


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

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Dec 12, 2005

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!
Dec 12, 2005

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
Dec 12, 2005

I GOT IT .......I GOT IT. Keep them coming!!!!
Dec 12, 2005

Haha...wish I was good at math...lolol anyways great and awesome job. 2 thumbs up
Dec 12, 2005

I'm no good at math, but great teaser! Maybe when I get good at math I will do this one over again!
Dec 12, 2005

I don't know if this is a Teaser or not. I did not know where to begin. How?
Dec 12, 2005

I'm with you precious!! Not to mention that my math skills are not up to par.
Dec 14, 2005

Nice one Shenqiang.
Jan 01, 2006

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.
Jan 02, 2006

I GOT it was hard though i figured it out because of 370
Jan 02, 2009

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!

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