Topic: 🤔🧩The Puzzle Thread🧩🤔 (Read 146 times)

Alright so here is the answer to Puzzle 2:

This one was supposed to be a lot easier, there is a total of 9 options for the leftmost digit since 0 cannot be in that place, and then 9 options for the second digit since 0 can now be included, then 8 and so forth. The solution becomes 9x9! which equals 3,265,920.

Adding a new Puzzle 2!:

Puzzle 2:
How many different 10-digit numbers, such as 7,829,034,651, can be written by using all 10 digits? Numbers starting with zero are excluded?

This one is a step away from the area of probability and might be easier for some!

What you’re describing is the solution to the Monty hall problem where the probability goes from 1/3 to 2/3 when you switch. This puzzle is different, well because you’re given the fact that one of the private keys revealed a bitcoin. Just with this statement you know that the probability of your wallet picked being the 2 BTC wallet is no longer 1/3.

Here are all the possible wallets with keys laid out but we don’t know which wallet is which.
Wallet1 key 1: 1btc
Wallet1 key 2: 1btc
Wallet2 key 1: 1btc
Wallet2 key 2: 1ltc
Wallet3 key 1: 1ltc
Wallet3 key 2: 1ltc

As soon as it’s revealed we have a private key with 1 btc in our wallet. We know it’s between wallet 1 and 2. Now if we look at what the odds are of being wallet 1 or 2, we would see that it’s 2/3 odds that’s it’s wallet 1 based on the fact that we know we found a btc key (there are 3 btc keys between wallet 1 and 2), hence wallet 1 has 2/3 cases where the btc was from and wallet 2 has 1/3 cases.

Now that we know that we have a 2/3 probability of us picking the wallet with 2 btc, it becomes pretty clear that switching would reduce it to 1/3 and therefore we should not switch!

Mainly each option will have 1/3 possibilities.
Wallet 1
1/3
Wallet 2
1/3
Wallet 3
1/3

but when you choose an option and the balance of another is revealed, the remaining option becomes 2/3 possibilities.

Wallet 1
2/3
Wallet2 (Your choice )
1/3

Wallet 3 (revealed)
0/3

Therefore it is always better switch.

Edit:
The probability of the discarded option is added to the free option, because you have chosen before with a probability of 1/3. Many mathematicians judged Monty Hall because you would think that the odds would be 50/50, but that is not the case.

Seeing someone else fascinated by the same interests as mine is a great feeling, Cheers!

I'll add some sources to the main post for the Monty Hall problem, I forgot that not everyone would have seen the problem before, although it is a popular one!
https://statisticsbyjim.com/fun/monty-hall-problem/

I won't provide an answer because, to be honest, I was unsure how to respond until I did some online research on the Monty Hall problem.

I just want to say that it was a fascinating and thought-provoking read. It's amusing how our logical thinking can sometimes clash with the mathematical principles of probability. Hats off OP for starting this thread. A great mental workout!

The Puzzle / Riddle Thread

Hi Everyone,

As a bitcoin enthusiast, I enjoy math and statistics along with cryptography. So in this thread, I would like to share my passion with all of you. I really enjoy solving puzzles that have some form of math in them. Puzzles like the Monty Hall Problem are my favourite. I'll be sharing some new puzzles / riddles here that I found to be enjoyable, hard to solve and challenging. I encourage anyone interested in these to try and solve them without any external help. Some / most of these will be tricky so try to think outside of the box.

In terms of answers, I'll update the main thread after a few days to post the answer. If one of you solve it with an easy to follow answer, I'll use that as the solution and mention you in the credits!

If anyone has any submissions to add to this list, please reply or send me a DM and I'll consider it. Note: It doesn't have to be bitcoin/ crypto related, any tricky puzzles and riddle's are welcome as long as they require some thinking to solve!

Good Luck!

You can click here to travel down to the current puzzle: Current Puzzle

---

Puzzle 1:
inspired by the monty hall problem
You are presented with three wallet.dat files. Each file contains 2 private keys. These private keys can hold either 1 Bitcoin or 1 Litecoin. Lets' not worry about address generation for now!

• One of the three wallets has 2BTC
• One has 1BTC and 1LTC
• One has 2LTC

You are not allowed to check the balances for each wallet and you have no way of knowing which wallet is which.

You are asked to choose one wallet as a prize. After you've chosen, your wallet file is imported into a desktop wallet and and one private key from your wallet is revealed. You find out that the key revealed holds 1 bitcoin. The wallet with 2LTC is taken out of the prize pool, and you are given the option to switch your wallet to the other remaining option.

Should you switch your choice??

Puzzle 1 Solution:

---

Puzzle 2:
Martin Gardner

How many different 10-digit numbers, such as 7,829,034,651, can be written by using all 10 digits? Numbers starting with zero are excluded?

Puzzle 2 Solution:
Will be posted soon!

---

Revision Log:

• 2023-09-27: Added a new Puzzle 2
• 2023-09-23: Added solution for Puzzle 1
• 2023-09-19: Revised some text in Puzzle 1 to clear up some ambiguity