21. Farmer Fi is selling chicken and duck eggs. She has baskets holding $4,6,12,13,22$ and 29 eggs. Her first customer buys all the eggs in one basket. Fi notices that the number of chicken eggs she has left is twice the number of duck eggs. How many eggs did the customer buy?
A 4
B 12
C 13
D 22
E 29
SOLUTION
E

The total number of eggs in Farmer Fi's baskets initially is $4+6+12+13+22+29=86$. Once she sells one basket, she notices that the number of chicken eggs she has left is twice the number of duck eggs she has left. Therefore, the total number of eggs she has left is a multiple of 3. Hence the number of eggs that were bought by the first customer has the same remainder when divided by 3 as the original number of eggs. Since $86=3 \times 28+2$, that remainder is 2 . Now 4,13 and 22 all have a remainder of 1 when divided by 3 while both 6 and 12 are multiples of 3 . However $29=3 \times 9+2$ and so has a remainder of 2 when divided by 3 . Therefore the first customer bought 29 eggs.