Are you smart enough?

Question

A bag contains 20 marbles. They are of three different colors. There are eight
blue marbles, seven red marbles, and five green marbles. You are asked to close
your eyes and draw marbles out of the bag, making sure you leave at least four
marblesof any one color, and at least three marbles of any second color.What is the maximum number of marbles you should draw?

Answer 1

answer is 7.

8b + 7r + 5g = 20 in all.

"leave at least 4 marbles of any one color, and at least 3 marbles of any second color"

if you took out all the lesser marbles (g+r), that's the worst case scenario.
if you somehow took out all the lesser marbles first, that is either the greens or the reds, then you would want to at least conserve 5 of the mixture of greens and reds, coz you'll know you'd have at least 3 of either color.

the mixture will have (5g+7r) = 12 marbles, and you'll let 5 of them in the bag to conserve the "2nd color >= 3" condition. so only able to draw 7 of them at most.

Answer 2

20

Answer 3

20

Answer 4

20

Answer 5

20

Answer 6

I would say 7. If you take eight, you might take out 5 red and 3 green, only leaving 2 red and 2 green, which doesn't follow the rule. If you take seven, there is no way you are not left with at least 4 of one color and 3 of a second.

Answer 7

Suppose your first 8 marbles are blue, then you draw four more marbles and two are red and two are green. The 13th marble will be either red or green.

13 is the maximum.

Answer 8

12

Answer 9

13

Answer 10

13