Braingle: '3-digit Numbers' Brain Teaser

3-digit Numbers

Math brain teasers require computations to solve.

Puzzle ID:	#27426
Fun:	(2.75)
Difficulty:	(2.56)
Category:	Math
Submitted By:	shenqiang

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 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 Dec 12, 2005	I GOT IT .......I GOT IT. Keep them coming!!!!
lorelle_b Dec 12, 2005	Haha...wish I was good at math...lolol anyways great and awesome job. 2 thumbs up
Brainy_1 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!
precious1026 Dec 12, 2005	I don't know if this is a Teaser or not. I did not know where to begin. How?
sweetmama Dec 12, 2005	I'm with you precious!! Not to mention that my math skills are not up to par.
chidam11 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 Jan 02, 2006	I GOT it was hard though i figured it out because of 370
javaguru 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!