There are 40 ways to make sums of three distinct positive integers total 25. (1+2+22 is such a sum, but 1+12+12 and 1+2+3+19 are not.)

How many different ways can three distinct positive integers sum to 1000?

Fill Column A with 664 1000's
Starting in B1 add a 1, in B3 add a 2, in B5 add a 3 etc. up to B663,
do the same with column C but start in C2, end in C664.
In the D column do D1=B1+1, D3=B3+1, etc,
Bear with me on column E, Starting in E2 insert 499, E4 = 498, E6=498, E8=497, E10=497, etc
Column F, Starting at F1 Sum A1-B1-D1, drag this to line 664,

You now have the minimum and maximum ranges for each initial digit, columns B+D+F =1000, as do C+E+F

Leave I1 blank, in I2 insert =E2-D1+1, highlight I1 & I2, then drag down to I664
Leave K1 blank, in K2 insert =IF(I2>1,I2,0), highlight K1 & K2, then drag down to K664
This will add up all of the values aloud in each range,
make M2=SUM((K2:K664)+1), this will give you the result you need.

82834.

Edited on July 22, 2004, 11:13 am

Posted by Juggler on 2004-07-22 11:06:05