Do you know the weighing mechanism that was used before the invention of the weight-controlled scale and the digital scale? This is a scale made up of two pans, so you can compare the weight of two objects, one on each pan.
The mechanism of this scale works as follows: if you put an object on the left plate that is heavier than the object on the right plate, the left side will be lower than the side of the right. If the objects are of equal weight, the scale will be in balance, that is, there will be no movement of the dishes.
Knowing this, solve the challenge Pedrinho faced.
Pedrinho was walking at the mall when he spotted a promotion that said “Solve the scale challenge and win a video game brand new." Pedrinho, who was a very smart and dedicated student, soon decided to see what the challenge was to try to win the video game.
The only information we have is that one of these balls is lighter than the others. The big challenge is to find out which ball is the lightest, weighing them only twice.
Try to solve this challenge without being afraid of making mistakes, as you will only understand how it is solved by trying.
As there are two plates, let's separate the balls into two groups: the first with six balls, and the second with two.
Group 1:
Group 2:
To continue the challenge, we must work with hypotheses, after all we are not actually testing the balls on the scale, so use all your imagination.
Weigh the first group.
When weighing the first group, two situations can happen:
1) All balls will have the same weight;
2) One of the plates will be taller, that is, the objects on that plate are lighter than those on the other plate.
So we must study each case, remembering that we can only weigh them one more time.
1st case: The First Group balls are all of the same weight.
If that happens, we are left with two balls, the balls in the second group. Certainly one of these balls will be the lightest, after all, the only information we have is that there is a lighter ball.
As we still have the right to weigh one more time, we will place each of the balls on the platters and weigh, for sure one of the platters will be higher and this will be the lighter ball.
2nd case: One of the dishes gets louder
If one of the dishes gets lighter, we know that one of the three balls on that dish is the one we want to find. We can only weigh one more time, so we will take two of these three balls and compare their weight. Again two things can happen.
1) The balls have equal weights.
If this happens, it means that the ball that was left out is the lightest ball. After all, one of the three balls is the lightest.
2) One of the dishes gets taller.
The plate that gets taller demonstrates that the lightest ball is the ball on this plate.
See that we only weighed twice, the only thing we had to do was separate the possible events.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
Kids School Team
