Announcing a Return to our Roots: The All-New Bitcoin Magazine

The 3 wallets problem


         The 3 wallets problem

This post was released for Issue 17 of Bitcoin Magazine as part of a series of articles about puzzles and games that started with Issue 12.

Here I present a few challenges for bitcoin hoarders, about keeping bitcoins in separate wallets according to some restrictions. Have fun solving them!

Suppose that I have 10 bitcoins and I want to store them in 2 separate wallets (A and B) without splitting coins (that is, not using fractional units). Keeping a wallet empty is allowed. It’s easy to figure out that there are 11 ways of doing so: (0,10), (1,9), (2,8), (3,7), (4,6), (5,5), (6,4), (7,3), (8,2), (9,1) and (10,0).

Figure 1: Example of legal distribution

 Challenge 1: Now suppose that I have 1,000 bitcoins¹. How many ways of distributing them among the two wallets are there?

 Now suppose that, for security reasons, I don’t want to keep more than 800 bitcoins in a single wallet.

Figure 2: Example of legal distribution.

Figure 3: Example of illegal distribution (there are more than 800 bitcoins in the right wallet).

 Challenge 2: How many ways of distributing those 1,000 bitcoins are there now?

Now suppose we add a 3rd wallet and I have no capacity restrictions. Remember that keeping some wallets empty is legal.

Challenge 3: How many ways of distributing those 1,000 bitcoins among the 3 wallets are there?

Figure 4: Example of a legal distribution for 3 wallets and 1,000 bitcoins.

Let’s add a capacity restriction of 800 bitcoins per wallet once again.

Challenge 4: How many ways of distributing those 1,000 bitcoins among the 3 wallets are there now?

Now for those that have cheated by using a computer to solve the previous challenges…

Challenge 5: How many ways of distributing 21 million bitcoins among 3 wallets with a maximum allowed capacity of 10 million each are there?

And now for those that have solved all the challenges so far, suppose that wallet A has a maximum allowed capacity of 5 million bitcoins, wallet B has a maximum allowed capacity of 10 bitcoins and wallet C has a maximum allowed capacity of 15 million bitcoins.

Challenge 6:  How many ways of distributing those 21 million bitcoins among the 3 wallets are there now?

And finally, let’s add a fourth wallet and remove the capacity restrictions.

Challenge 7:  How many ways of distributing those 21 million bitcoins among the 4 wallets are there now?

Please post your answers in my forum:

... and I will reward the best post with a copy of one of my games. I’m looking forward to discussing your findings. Thank you for reading and for your donations! 

You might also enjoy my previous posts:

- Bitcoinstellations

- Rise of the machines- Creativity as problem solving- The Bitcoin Maze- The Bitcoin Harvest------------------------------------------------------------------------------------------1. Unfortunately I don't!  


Bitcoin Price Analysis: Blowing Through Support Levels on the Way to $3,000

Bitcoin continues to tumble lower and lower as it struggles to claim any footing in the market. It’s down almost 50% in three weeks and it’s showing very little sign of stopping. It’s currently clutching onto the $3,500 values but it doesn’t look like it can hold on much longer.

Bitcoin Schmitcoin

Op Ed: SEC’s Latest Declaration Creates Legal Minefield for Digital Assets

This broad, authoritative declaration is not unexpected, as, to date, the SEC has stated that all digital assets — regardless of whether they function as alt coins or utility tokens — are securities at least initially and, thus, subject to its jurisdiction.

Huhnsik Chung and Nicholas Secara

Op Ed: Cryptocurrency’s Unrealized Opportunities for U.S. Tax Professionals

Tax accountants and firms that specialize in cryptocurrency will emerge to capture and service this market. The first movers will be the ones who stand to capture the oversized profits.

David Kemmerer

Op Ed: Anatomy of the Tether Attack: Are Stablecoins Vulnerable?

Last month's attack on Tether contains a cautionary tale: Only those coins that can survive such attacks have the slightest chance of becoming the “holy grail" of stablecoins.

Henry He