1. cards

Box A and box B have 6 cards each. Each card is marked with one integer, 1 through 6. Both boxes can have more than one card with the same integer, but the sum of all the integers in each box must be 18. Two of the cards in box/1 are 6's and two of the cards in box B are 5's. If one card is drawn from box A and one from box B, but neither a 6 nor a 5 is drawn, what is the largest possible sum of the integers on the cards drawn from the two boxes?
A.
3
B.
4
C.
7
D.
8
E.
12

2. Originally Posted by mths
Box A and box B have 6 cards each. Each card is marked with one integer, 1 through 6. Both boxes can have more than one card with the same integer, but the sum of all the integers in each box must be 18. Two of the cards in box/1 are 6's and two of the cards in box B are 5's. If one card is drawn from box A and one from box B, but neither a 6 nor a 5 is drawn, what is the largest possible sum of the integers on the cards drawn from the two boxes?

A.
3
B.

4
C.

7
D.

8
E.

12

Assuming exactly 2 sixes in Box A and exactly 2 fives in Box B:

To put the largest number on the cards and still have 6 cards in each box:

Code:
Box A            Box B
-----            ------
6                   5
6                   5
3                   4
1                   2
1                   1
1                   1
Largest sum = 7

3. Hello, mths!

There is no formula for this problem.
. . We just have to talk our way through it.

Box A and box B have 6 cards each.
Each card is marked with one integer, 1 through 6.
Both boxes can have more than one card with the same integer,
but the sum of all the integers in each box must be 18.
Two of the cards in box A are 6's and two of the cards in box B are 5's.

If one card is drawn from box A and one from box B, but neither is a 5 or a 6,
what is the largest possible sum of the integers on the cards drawn from the two boxes?

. . $(A);3 \qquad (B)\;4 \qquad (C)\;7 \qquad (D)\;8 \qquad (E)\;12$

Box A has two 6's. .The other four add up to 6
There are two choices: . $\{{\color{red}3},1,1,1\},\;\{2,2,1,1\}$

Box B has two 5's. .The other four add up to 8.
There are three choices: . $\{{\color{red}4},2,1,1\},\;\{3,2,2,1\},\;\{2,2,2,2 \}$

Selecting the largest from each box, we get: . $3 + 4 \;=\;{\color{blue}7}\quad\hdots$ answer (C)

Too fast for me, masters!
.