document.write( "Question 540914: Only four integers between 100 and 1000 equal the sum of the cubes of their digits. Three of these are 153, 370, and 407. What is the fourth? \n" ); document.write( "

Algebra.Com's Answer #354005 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Lucky for us, we got those 3 numbers.
\n" ); document.write( "The problem tells us that for 370, the sum of the cubes of the digits is
\n" ); document.write( " $\"3%5E3%2B7%5E3%2B0%5E3=3%5E3%2B7%5E3=370\"$
\n" ); document.write( "Then, for 371, the sum of the cubes of the digits must be
\n" ); document.write( " $\"3%5E3%2B7%5E3%2B1%5E3=3%5E3%2B7%5E3%2B1=371\"$
\n" ); document.write( "BINGO!
\n" ); document.write( "The fourth number is 371.
\n" ); document.write( "No, I did not realize immediately.
\n" ); document.write( "I found it through a lot of logical work
\n" ); document.write( "After I found it, I immediately realized that it was so obvious (in hindsight) that if one of the solutions ended in zero, the next integer would also be a solution.
\n" ); document.write( "That is the kind of question that would be easily answered by a 13-year old in the artofproblemsolving forum. (That's full of kids with at least semi-realistic hopes to get to the Math Olympiad). \n" ); document.write( "

\n" );