You have nine apples which all look identical.
One of them is slightly heavier than the rest.
You have a pair of weighing scales.
What is the LEAST number of times you would have to use the scales to guarantee that you will identify the heavier apple?
Answers and explanations in the COMMENTS below please.
Three times
ReplyDelete1. Weigh 8 of the apples. Put 4 of those in one side and the rests in the other side. If the weighing scales show that both of those 4 apples have the same weight. It means that one apple that you don’t put into the weighing scales is the heaviest one.
2. If the weighing scales shows that the weight of 4 apples in the left are different from the weight of 4 apples in the right side, take the heavier one. Then divide those (the heavier one) into two part (both of those consist of 2 apples) and put into the weighing scales again.
3. If the weighing scales shows that the weight of 2 apples in the left are different from the weight of apples in the right side, take again the heavier one. Then divide those (the heavier one) into two part. Put one apple in the left side and the other one in the right side. You can find the heavier one now.
i think it will take at least 8 times.
ReplyDeletetake one apple as a referers and start weighing all the apples and record their weighs. you'll find the heavier pretty soon.
First, divided the eight apples become two parts. Each parts have four apples. Then, weigh them.
ReplyDeleteSecond, after weigh each parts you will know which sides are heavier. Weigh heavier part and divide it become two parts. It's consist of two apples in each side.
Third, finish weigh each parts you will know which sides are heavier. Divide it into two parts again. It's side consist of an apples.
Finally you will know the heaviest apple. It's just take three times.
@everyone (so far). You're all wrong. Less than 3 times!
ReplyDeleteThis comment has been removed by the author.
ReplyDelete1. Divide the apples into 3 groups. Each Group consists of 3 apples.
ReplyDelete1st Group : a,b,c
2nd Group : d,e,f
3rd Group : g,h,i
(assume that the names of the apples are: a,b,c,d,e,f,g,h,i)
2. Put the 1st Group and 2nd Group of apples on the weighing scales. If they are balance, take 2 apples from the 3rd Group, put one into the 1st Group and one into the 2nd Group. For instance: I put apple 'g' into the 1st Group and apple 'h' into the 2nd Group. If they are still balance, it means that apple 'i' is the heavier one.
So, i think it will take 2-3 times of using the scales to find the heavier apple.
I want to revise my statement above, it definitely only needs 2 times of using the scales to find the heavier apple. Just 2 times!
ReplyDelete(Thanks to Bram for making me realise it)
Just adding to Dani's solution, there is a slight change to make it only 2 steps:
ReplyDelete1. Put the 1st group and 2nd group of apple on the weighing scale. If the scale shows one of the group is heavier, then the heavier apple is within that group. If not, then it is in the 3rd group. Either way, we got ahold of the group that apple is in.
2. Take 2 apples from the group and put them on the weighing scale. If the scale show one of the apple is heavier, then that apple is the heavier one. If the scale is balanced, then the apple that is not on the scale is the heavier one.