Harry Potter: Don't touch

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- Okay, three chests, the first is diamonds, the second is rubies, the third is half of both. Two kinds of gemstones. The intruder took the rubies. Which chest could he have done it from? Certainly not the first one, we can cross that one off, it's diamonds. It's not necessary. The second and third had rubies, so he must have opened one of those chests. Let's say he opened the second chest and there are only rubies there, so after taking half of the ruby chest, there are still rubies there. If he opened the second chest, the answer is rubies one hundred per cent, diamonds zero per cent. However, there is also a third chest that has both, there are two kinds of gems. If you take rubies from there, there will be diamonds, so when you open the third chest, the probability of taking rubies is zero per cent and diamonds is one hundred per cent. Now the total probability, if I don't know which chest I'm going to open, then after taking rubies from there with fifty per cent probability there will be diamonds, and similarly with fifty per cent probability there will be diamonds.

- Is that the answer?

- I don't know... Well, logically, yes. But the riddle's a little too easy to be a sphinx riddle. There's no catch? The intruder opened a random chest? Did he pick up the stone really at random? Did he come back for the rubies? Or just for the jewellery? Could the contents of the chosen chest have somehow influenced his actions?

- There's no catch, but if you're not stupid.

Listen to me again, my brave young friend.

- He opened the first chest he could find.

He stuffed his pockets with a certain kind of stones like a chipmunk.

These stones happened to be rubies.

They won the man's heart.

Only half a soundouk could fit in his pockets.

For the intruder, the burden was too great.

After selling the jewellery, he went back.

The rest of the wealth was collected carefully.

Opening the same chest, he took the rest of the stones.

The question is, what were these stones?

You can't give an exact answer, you need probability.

Which stones did the intruder's greed take away this time?

- Collect the rest of the wealth carefully. Not the rubies. Okay, I get it, I'll think about it some more.

Harry didn't know how to fight sphinxes. He had read that they were formidable opponents that only strong wizards could tame. If he got the answer wrong, his third challenge would end right there. It would take a couple more times to analyse the task.

For some reason, the first chest with all the diamonds was bothering him. It was too useless. There's no way that part of the condition should just be ignored. So. First chest. Just the diamonds. The intruder picked up a ruby at random. The first chest obviously wasn't opened. And if it was? Let's say he opened the first chest, and there are diamonds in there, so he took a diamond from there, not a ruby. But the condition says he took the ruby...

That doesn't make any sense...

The first chest is really useless. You can't take a ruby from a chest full of diamonds. The second chest - rubies, it's simple, you open it, take any stone, it is in any case - a ruby. Third chest... Hmm. Diamonds and rubies. Equal amounts. How many are there? Suppose a thousand of those, a thousand of the other, taking the nearest stone, the intruder... I wonder if he took the nearest stone?

- Were there stones mixed up in the third chest? Or were some stones closer than others?

- The condition doesn't say.

Mm-hmm. However, lack of information is also information. Even if one type of stones was closer to the intruder than others, it still won't be possible to determine which gems were closer. And anyway, was it said that a random stone was taken or....

- Did the intruder start picking up a random type of gem? Or the closest one?

- He opened the first chest he could find.

Started stuffing his pockets with a certain kind of stone, like a chipmunk.

These stones happened to be rubies.

They won the man's heart.

- Yeah, same thing again. Lack of information. Well, that makes sense. Fifty per cent, why not fifty per cent?

- Is that the answer?

Harry thought again. He was plagued by doubts. That's not how sphinxes should ask riddles. It's too easy! Freshmen and those would solve it! There must be a catch, but there didn't seem to be one. By all laws of logic, the answer is fifty per cent, three chests, one has a red and a blue stone, the other has two red stones, the third has two blue stones, the unknown person opened a random chest and took a red one, that is, if the chest is the first, the next stone will be blue, if the second, then red. The probability of opening the chests is the same, the person opened a chest at random, not a certain one. The answer should be fifty per cent, but that's too easy. Moody used to do this all the time in times of testing attacks, put out some simple clue that was actually a trap.

- Sphinx, I haven't solved the riddle, but I know the answer isn't fifty per cent, I don't know why, but I do. Can I go further if I give the answer that the probability is 'not equal'?

- Such a perceptive brunette,

He's got to give an accurate answer.

- Can I... Well... Not give an answer and go back? There's another fork in the road, that way you can reach the labyrinth too.

- If you can't solve the riddle.

You can go back without any trouble.

But know that if you can look behind my back.

you'll find a shortcut to the cup.

A shortcut, huh? How short? Straight to court three? Even 15 minutes would be a big help. At that fork, Bagman's map cuts off, and a shortcut could theoretically exist. But in order to get any further, we need to solve a bloody mystery.

Okay, let's say Harry Potter came to the three chests. Well, not just one Potter, but three of them. They each open one chest. And they each have to get a ruby. All three Harry Potters stuck their hand into their chests and pulled out a random stone, one Harry Potter was unlucky, he opened a chest of diamonds, he can be crossed off. Another Potter was lucky, he got a ruby from the ruby chest. Well, the third Potter... What he got is unknown... Hmmm.....

No, it's not. Six Potters, two for each chest, two got diamonds from the chest with diamonds, remove, two got rubies from the chest with rubies, take into account, one got rubies from the chest with diamonds and rubies, add, another got diamonds from the chest with diamonds and rubies, he is not needed. Thus, there are three Potters who got rubies, two took rubies from the chest with rubies, so the other half also rubies, and the other took rubies from the chest with diamonds and rubies, so there are still diamonds. Total, two Potters take the rubies after returning, and one Potter takes the diamonds.

- Sixty-six per cent on taking the rubies, and thirty-three per cent on taking the diamonds.

- Is that the answer?

- Well... No. Now...' Harry hesitated again.

Why is the answer two thirds more correct than half... After all, if a ruby was taken, then... Aha! That's where the mistake is. Analysing the terms of the problem. The rubies have already been taken from the chests. If we ignore the condition and take it as an immutable truth, the answer is fifty per cent. When the intruder took the ruby from the chest, he had already predetermined the probability. After all, there are one and a half chests of rubies in the three chests, and the intruder took half, that is, one third of the total stock, and this third he was more likely to take from the chest completely full of rubies.

- Yes, that's the answer. A probability of sixty-six and thirty-three per cent.

The sphinx smiled and stepped back from the aisle.

- Right, onwards with....

Harry didn't bother to listen to the continuation of the sphinx's line, he ran down the vacated aisle with all his might. He had taken too long to solve the riddle and had fallen a little behind... Or, on the contrary, it was quite possible that he was ahead of his opponents by completing the task. Either way, we must hurry.

* * *

Harry had been walking for half an hour and still no boggart. That was odd. By the rules, Harry was not allowed to know the location of his opponents, but Bagman had made it clear - one way with the boggart and the sphinx, the other with the phoenixes and the redcaps. Potter had met and passed the sphinx, so there must be a boggart around here somewhere. But where is it?

Fifteen minutes into the journey, the maze began to divide. The number of forks doubled compared to the first part, and since, unlike the beginning, this part of the labyrinth was not on the map, Potter was constantly hitting dead ends. After failing to find his way out for the seventh time, Harry decided to stop wandering and use a spell he knew of to break through the maze wall to go north.

- Nulus venificium ager! - Potter pointed his wand at the maze wall and jumped through the resulting holes, moving between passages.

It was unlikely that the organisers had considered this way of moving through the obstacles when creating the maze, it was far too efficient. After five minutes, Harry found himself in unfamiliar passages that he hadn't reached before.

After another jump over a wall, Harry found himself nose to nose with a matured Piers Polkiss. Such an unexpected encounter came as a shock to Potter, he forgot about the boggart, forgot about the test, forgot about almost everything. The only thought in his mind was, 'Piers has come for me!'

- Stupefy! - Harry shouted, jumping away from Piers.

He didn't react in any way to the spell he released, it somehow flew through him. Pierce smirked and began to move slowly towards Harry.

- Incendio! А! Bitch, what do you want from me!!! - Shouted Potter, dodged Polkiss' arm and tried to run away from the oncoming Pierce.

It wasn't ten seconds later, however, that Harry stumbled into a dead end. Pierce was closing in.

- No! Stay back! I'll kill you! - Potter shouted, pointing his wand at Piers.

The man ignored Harry's words and continued to slowly walk towards him.

- Stop, you creature! Seko! Seco! - A dark slashing curse flew through Pierce. - Why isn't it working?! Stay back! Avada Kedavra!

The killing curse didn't work. Potter's wand wasn't going to send a green beam out.

- Why didn't it work! I hate you! Why... Stop-Stop-Stop-Stop-Stop... You're a boggart!

His brain was almost successful in its attempt to reach its owner, but Pierce was so close that Harry had lost all ability to think rationally and, even though he knew he was a boggart, he couldn't regain his composure! He couldn't remember what spell was supposed to kill boggarts; the only thing he could remember was that it started with an 'r'.

- Rictumsempra! Reparo!

And those curses went through Pierce as well.

- Nulus venificium ager! - Harry punched through the wall of the maze and jumped out onto the path of the neighbouring passage.

Then, finally succumbing to panic, he ran for wherever the hell he was going.