Problem:
Which terms must be removed from the sum
21​+41​+61​+81​+101​+121​
if the sum of the remaining terms is to equal 1?
Answer Choices:
A. 41​ and 81​
B. 41​ and 121​
C. 81​ and 121​
D. 61​ and 101​
E. 81​ and 101​
Solution:
21​+41​​+61​+81​+101​+121​=12060​+12030​+12020​+12015​+12012​+12010​​
Since 60+30+20+10=120, it is clear that one may remove 12015​=81​ and 12012​=101​. Furthermore, one sees easily from the right hand side above that no other terms sum to 12027​. Thus one must remove 81​ and 101​.