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3-digit Numbers

Math brain teasers require computations to solve.

 

Puzzle ID:#27426
Fun:*** (2.76)
Difficulty:*** (2.56)
Category:Math
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:

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.

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Comments

Jimbo*au*
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!
wolfmanh**
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
redraptor50*us**
Dec 12, 2005

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

Haha...wish I was good at math...lolol anyways great and awesome job. 2 thumbs up
Brainy_1Aus*
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!
precious1026Aus*
Dec 12, 2005

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

I'm with you precious!! Not to mention that my math skills are not up to par.
chidam11Ain*
Dec 14, 2005

Nice one Shenqiang.
mr_brainiac*
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.
trickyone*ca*
Jan 02, 2006

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