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.
I think the answer should be at least 2 times! First of all we need to separate the apples into 3 groups which are consisted with 3 apples each. We will give each group a name, for example A, B, and C. Then, we need to use the scales to compare 2 groups of apples. From this step, there will be 2 different outcomes. Whether the scale will show balance result, or one side would be heavier than another one. Therefore we will know which group that contains that one heavier apple. For example if we compare A and B and it show balance, the heavier apple must be in C, if either A or B heavier that means the one that contains heavier apple must be there.
ReplyDeleteFrom here, we just need to do 1 more little step. If we already know which group contains that heavier apple, we will compare two put of three apples. More or less the method will be the same as the first measurement. If the result is balance, the heavier apple must be the one that is not in the scales and if the scales leaning to one of the side, gotcha! I think that is the least amount we need to use the scales to find the heavier apple!
I think that you need to use at least two times the scales to find the heavier apple. First you have to separate the apples into three groups of three apples. Then you place one group on each side of the scale. If you see that one side is heavier than the other, then the heavier apple is in that group. If the scales don’t move, the heavier apple is in the third group. Now that we have identified in which group is the heavier apple we just have to find which one of the three apples is the heaviest. For that we do the same procedure once again, but that time the three apples represents the three groups. So that time, we place two of the three apples on each side of the scales. Of course, if one of these two apples is heavier that the other, we will observe the result immediately. And if the scales are balanced, the heavier apple will be the one that we didn’t place on the scales.
ReplyDeleteTwo times of weighing is enough to determine which one is the heaviest apple. Starts by dividing the nine apples into three random groups. Pick whatever two groups amongst, use the scale to know both group’s weight. The first possibility is when one group is heavier than the other, than the heavier one should contain the heavier apple (let’s just call it the special group). The second possibility must be both groups weighing the same, then the rest one group must be consisting the heavier apple (the special group in the second possibility). Take two random apples from the special group on whatever possibility happening and use the scale again. If one of the apple is heavier, then that’s the one we’re seeking for. If both apple weigh the same, then the last apple must be the slightly heavier one.
ReplyDeleteExcellent. Well done all of you.
ReplyDeleteThe least amount of time you need to use the scale is twice. Separate the nine apples into three different groups (each group contain 3 apples) then indicate them by using either group ABC or group 123. Use the scale for the first time to know which group has heavier apple (e.g. group A and B are weighed, then the scale on group B turns out to weigh heavier than group A, thus we know that group B contain the heavier apple) or if the scale shows the same weight, we can conclude that group C contain the heavier apple. Use the scale for the second time after we know the group that contain the heavier apple, take two random apples. If the heavier apple are on the scale, it will show on the scale, if the scale shows the same weight, we can conclude that the heavier apple is the last apple that is not weighed down.
ReplyDelete