This riddle takes place between a band with thousands of fans and their manager. The members of the band are so messy and disorganized that their manager gets fed up with it one day and wants to teach them a big lesson.
The band members try to find their instruments in the puzzle prepared for them, but the probability is extremely low. To solve the riddle, you must think strategically and carefully consider each step.
There’s a band, they play great, but they’re terrible at being organised.
When the band members go on tour, they always put instruments in unrelated places, and the resulting confusion drives their managers insane every time.
One day, they are about to go to one of their biggest concerts, and the band suddenly finds themselves in a windowless and soundproof studio instead of backstage. With their hands tied.
Turns out their manager wanted to teach the band members a lesson. The whole thing starts here.
The group’s manager explains this strange situation as follows: All deals are canceled if the group members do not learn to organize. They can’t go to this concert or their next concert.
There are 10 large boxes out there, each with an instrument of one of the 10 members of the band, with pictures of the instruments on the boxes. But these pictures are placed randomly, not according to what’s inside the boxes.
The manager says he’ll let each member in one at a time and they can each look inside five boxes.
They cannot touch the instruments or tell others what they found in which box. They cannot tick the boxes, give information to their friends, and tell them what they see by making secret signs.
If each manages to find their own instrument, they can go to the concert tonight. Otherwise, both their managers and companies will stop working with them, and the concert will be cancelled.
They have 3 minutes to think and plan before they start.
The group is in despair. The chances are incredibly low.
Each musician has a 50% chance of finding their instrument by choosing five boxes at random. But the chances of all members succeeding at the same time are even lower, 1 in 1024.
But suddenly the drummer comes up with an idea that has a higher than 35% chance of success. Can you find out what this plan is?
If you’re ready to learn the answer, you can take a look below.
The drummer’s plan is this: Everyone will first open the box with the picture of their instrument. If the instrument is inside, there is no problem anyway. He succeeded.
If not, he’ll look at what’s inside and then open the box with a picture of what’s inside. It will continue like this until you find your instrument. Thus, the probability of success will be significantly increased compared to going in a random order.
According to the probability calculation, this plan will work perfectly and the band members who manage to find all the instruments will be performing in front of thousands of fans in a few hours.
So how exactly does this plan work? From here on out, math nerds keep their ears up.
Everyone will first open the box with the picture of their own instrument on it, then the box with the picture of the instrument inside the box they opened, then the box with the picture of the instrument in the box they just opened, and when this continues, this sequence will have returned to the beginning at some point.
This system works much better than random guessing. Because each musician restricts himself to a certain cycle when he starts with the box with the picture of his instrument on it.
So how do we calculate these probabilities?
To understand this, let’s consider a slightly simpler scenario than the puzzle at hand, only 4 instruments and 2 choices for each musician.
Let’s see what the odds are for each musician to fail. For it to fail, it must find what it’s looking for not the first or the second time, but the third or fourth time. It means that there is a possibility to choose 6 different ways in 4 boxes in front of him.
One way to understand this better is to draw a square, placing an instrument at each corner and connecting the opposite corners.
So you can see how many different paths you can draw on these lines.
Remember that no matter which corner it starts from, the arrow is considered the same as long as it continues in the same direction. But these two below are different from each other.
Here we can see eight different triple loops that take the shape of a triangle. When you proceed in the form of a triangle, that is, a triple selection, instead of a square, that is, a quadruple selection, you will see four triangles and two different paths depending on which instrument is left out.
Of the 24 possible box combinations, 14 will set you up for failure and 10 will set you up for success.
This calculation method always works very well when the number of musicians is even.
To put it in a shorter and more technical way, we come across an equation like this.
When there are 10 musicians, the probability is around 35%.
What if there were 1,000 musicians, even 1,000,000?
The probability approaches about 30% as the n numbers in this equation, i.e. musicians and equipment, increase.
So the result is not guaranteed, but it is a solution that increases the chances of the musicians tremendously.
As a result, where is 1 in 1024, where is 35%…
61766
