You have 27 cupcakes, they all weigh exactly the same, but one. Ths one has a key inside it, it looks exactly the same as the others, but weighs more.
You have a balance. A balance is a scale that works like a see-saw. You put an object on each side and it tilts for the heavier side.
Anyway...
What is the least number of times it takes to use the balance, to find the cupcake that weighs more?
In other words...how many times do you have to use the balance, to find the cupcake that weighs more? The least amount of uses.
2007-01-22 14:02:10 · 7 answers · asked by Jesse B 2 in Science & Mathematics ➔ Mathematics
You can do it in 3:
(1) Put 9 on each side of the scale. If one group of 9 weighs more, keep that 9. If they balance, take the 9 not used in the weighing.
(2) From the 9 left, put 3 on each side of the scale. If one group of 3 weighs more, keep that 3. If they balance, take the 3 not used in the weighing.
(3) From the 3 left, put 1 on each side of the scale. If one weighs more, that is the heavy one. If they balance, the heavy one is the one not used in the weighing.
* * * * *
Ah, Ronin, I see you like my answer....
LOL, I see the first poster does also. Quite amusing how everyone is in agreement now...
2007-01-22 14:12:32 · answer #1 · answered by Anonymous · 1⤊ 0⤋
3 uses will do the trick.
Divide the cupcakes into three groups of 9 and compare two of the groups. If they balance, the key is in the group you haven't tested. If they don't balance, it's in the heavier group.
Then divide the group of 9 containing the key into three groups of three and repeat. Then do the same thing again to determine which cupcake is the heavy one.
2007-01-22 22:23:46 · answer #2 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
The least amount of times would be one. If you put 13 cupcakes on each side for a total of 26 and the balance remains even, then the leftover cupcake has the key.
2007-01-22 22:09:02 · answer #3 · answered by turcott2 2 · 0⤊ 1⤋
3 times.
you divide the 27 cupcakes into 3 groups each containing 9.
( first Weighing)
Then weigh the first and second group.If they both weigh the same, then the third group contains the cake with the Key.
If they dont weigh the same, then the heavier one contains the cake with the key.
(Second weighing)
Then take that group which contains the key and seperate them into 3 groups containing 3 each.
Weigh any of the 2 groups.If they weigh the same,then the other group contains the cake with the key.
If they dont weigh the same,then the heavier one contains the cake with the key.
(third weighing)
Take that group which contains the cake with the key.Seperate them into 1 , 1, 1.Weigh any two.
If they weigh the same the other one is the cake with the Key.
If they dont weigh the same, Then the heavier one is the cake with the key.
2007-01-22 22:06:20 · answer #4 · answered by sg 2 · 0⤊ 2⤋
1 is the least possible. 3 is the best possible answer.
Place 13 on one side, 13 on the other, leave one off. If it balances, the left off one has the key.
If not balanced, take the side that was heavier. Place 6 on one side 6 on the other, and one off to the side. If it balances the one off to the side has the key.
If not balanced, take the heavier side. Place one on each side and one off to the side. If it balances, the one off to the side is heavier. If not, the heavier side has the key.
2007-01-22 22:11:29 · answer #5 · answered by JEBalke 2 · 0⤊ 1⤋
3 weighings
do 9 and 9 leaving 9 out
if one side is heavier get rid of all the rest. Or if they are even, keep the 9 you left out and get rid of all the rest.
Weigh 3 and 3 leaving 3 out, see above
Weigh 1 and 1, see above.
Oh SG, you so did not have that answer until I posted it. You had 4.
2007-01-22 22:10:52 · answer #6 · answered by Anonymous · 1⤊ 1⤋
if i'm mot mistaken...3 times
by grouping them to 9s first..then to 3s..then lastly, you get the heaviest...
2007-01-22 22:13:18 · answer #7 · answered by swas77 2 · 0⤊ 0⤋