# Faulty logic when summing large integers?

This is in relation to the Euler Problem $13$ from http://www.ProjectEuler.net.

Work out the first ten digits of the sum of the following one-hundred $50$-digit numbers.

$37107287533902102798797998220837590246510135740250$

Now, this was my thinking:

I can freely discard the last fourty digits and leave the last ten.

$0135740250$

And then simply sum those. This would be large enough to be stored in a $64$-bit data-type and a lot easier to compute. However, my answer isn't being accepted, so I'm forced to question my logic.

However, I don't see a problem. The last fourty digits will never make a difference because they are at least a magnitude of $10$ larger than the preceding values and therefore never carry backwards into smaller areas. Is this not correct?

• I think you're counting from the wrong end... – Scott Morrison Jul 20 '10 at 20:33
• This problem is actually small enough to use a BigNum implementation, like BigInteger in .NET 4.0. – John Gietzen Jul 20 '10 at 20:33
• @Morrison: What do you mean? The smallest numbers always start at the right? @Gietzen: I think I'll try that with my next approach, thanks for the idea. – IAE Jul 20 '10 at 20:37
• "First" is ambiguous. Ten leftmost or ten rightmost? I believe the people at Project Euler want the former. – badp Jul 20 '10 at 21:05
• They are asking for first ten digits so you need to calculate the whole answer and then show the first 10 digits as answer – Himadri Jul 22 '10 at 5:06

9999999999