14. Eight unmarked envelopes contain the numbers: $1,2,4,8,16,32,64,128$. Eve chooses a few envelopes randomly. Alie takes the rest. Both sum up their numbers. Eve's sum is 31 more than Alie's. How many envelopes did Eve take?
A 2
B 3
C 4
D 5
E 6
14. D The sum of the numbers in the envelopes is 255 . Let $E$ be the sum of Evie's numbers. Then Alie's numbers will have a total of $E-31$. Hence we have $E+(E-31)=255$, giving $2 E-31=255$, so $2 E=286$ and $E=143$. The only way to add up powers of two to get 143 is $128+8+4+2+1$, so Evie took 5 envelopes.