Your task: Devise a plan to guarantee your survival.

Question

You are taken prisoner and given 12 gummy bears. All of the gummy bears are poisoned except for one. At the end of your third day in captivity, you must eat one of the gummy bears. The good gummy bear either weighs slightly more or less than all the others, but the difference is so infinitesimal that it is impossible to tell by any other means than with a super sensitive scale, which you are allowed to use once per day.

 

Your task: Devise a plan to guarantee your survival. In other words, come up with a plan in which you may use the scale no more than three times to find out which gummy bear is safe to eat.

 

The scale is a balancing scale.

Answer 1

If I know that the poisoned gummy bear weighs less than all the others I can solve the problem, or if I know that the poisoned gummy bear weighs more than all the others I can solve the problem also. I will assume that the gummy bear that is poison weighs more than all the others. The solution is the same if the gummy bear weighs less than all the others.

put 3 gummy bears on one side and 3 gummy bears on the other side of the scale

if they weigh the same, the poisoned one is with the other 6 (1 weighing)

now put the other 6 on the scale, 3 on one side and 3 on the other

the side of the scale that goes down contains the heavier poisoned gummy bear (2 weighings)

you know that one of the 3 gummy bears on the side that went down is poisoned

take any 2 and weigh them

if the scale balances, then the one left over is poison

if the scale doesn't balance the side that goes down contains the poisoned gummy bear (3 weighings)

if on the first weighing, the scale doesn't balance, you know the poisoned gummy bear is on the side that goes down

you then take any 2 and weigh them and I have already explained what to do in this case