2000 PMWC Problems/Problem I15: Difference between revisions
Created page with "==Problem== The sum of several positive integers is <math>20</math>. Find the largest product that can be formed by these integers. ==Solution== ==See Also==" |
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==Solution== | ==Solution== | ||
Try <cmath>5: 2*3*4*5*6 = 720</cmath> | |||
Try <cmath>4: 3*4*6*7 = 504</cmath> | |||
Try 3, then realize it's going to be smaller. | |||
6 numbers is too many, since <cmath>1+2+3+4+5+6=21</cmath> | |||
Thus the answer is 720 | |||
==See Also== | ==See Also== | ||
Latest revision as of 13:26, 31 January 2017
Problem
The sum of several positive integers is 
. Find the largest product that can be formed by these integers.
Solution
Try ![\[5: 2*3*4*5*6 = 720\]](http://latex.artofproblemsolving.com/1/1/c/11c22eb0174181ecd2c30a1d2d27b88d1639ddac.png)
Try ![\[4: 3*4*6*7 = 504\]](http://latex.artofproblemsolving.com/4/5/3/453667a07be111ae92326dca9b4f7a0f081da41d.png)
Try 3, then realize it's going to be smaller.
6 numbers is too many, since ![\[1+2+3+4+5+6=21\]](http://latex.artofproblemsolving.com/7/c/e/7cea75cd91286e850ef4923b19782b463dc49be2.png)
Thus the answer is 720
