Help with this problem please

Jun 2010
2
0
Ok, this is another one of those problems that for some reason just doesn't make any sense to me; it seems obvious but the actual answer is contradictory to what I thought was right. Here it goes,

"Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?"

I thought, "Ok, there are 8 red jellybeans, but only 4 green and 4 blue jellybeans...so that means that there has to be 4 red and 4 green and 4 blue jellybeans that are taken out of her pocket to reach the minimum number of jellybeans to ensure that she has one of each color" in reality, the answer for this problem is 13. Thirteen?? Where the hell did that number come from??? I just don't understand why this is the answer. Perhaps someone could enlighten me.(Headbang)
 

Ackbeet

MHF Hall of Honor
Jun 2010
6,318
2,433
CT, USA
This is the pigeonhole principle. What if the first 8 jelly beans were red? And, in addition, what if the next 4 jelly beans were either all green or all blue? You still don't have one of each color in that case! You'd have picked 12 jelly beans, but without getting one of each color. However, picking one more jelly bean ensures you'd get one of each color.
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
Ok, this is another one of those problems that for some reason just doesn't make any sense to me; it seems obvious but the actual answer is contradictory to what I thought was right. Here it goes,

"Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?"

I thought, "Ok, there are 8 red jellybeans, but only 4 green and 4 blue jellybeans...so that means that there has to be 4 red and 4 green and 4 blue jellybeans that are taken out of her pocket to reach the minimum number of jellybeans to ensure that she has one of each color" in reality, the answer for this problem is 13. Thirteen?? Where the hell did that number come from??? I just don't understand why this is the answer. Perhaps someone could enlighten me.(Headbang)
Consider the worst case:

She took out all 8 red jellybeans and then - worst as it could be - she took out all 4 green jellybeans. When she take out another jellybean (there are only blue ones left) she has indeed at least one jellybean of each color: 8 + 4 +1 = 13.
 
Nov 2009
717
133
Wahiawa, Hawaii
to insure that all 3 colors are selected, the remote possibility of all the reds and all the greens or all the blues are selected plus 1 of greens or blues as an example:
8reds + 4greens + 1blues = 13

Edit: to late again