{"id":29226,"date":"2014-02-08T04:09:52","date_gmt":"2014-02-08T04:09:52","guid":{"rendered":"http:\/\/ci027cfe78001c2697"},"modified":"2025-01-28T20:56:48","modified_gmt":"2025-01-28T20:56:48","slug":"3-wallets-problem-1391832592","status":"publish","type":"post","link":"https:\/\/bitcoinmagazine.com\/technical\/3-wallets-problem-1391832592","title":{"rendered":"The 3 wallets problem"},"content":{"rendered":"
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This post was released for Issue 17 of Bitcoin Magazine<\/a> as part of a series of articles about puzzles and games that started with Issue 12<\/a>.<\/em><\/p>\n

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

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\u2019s 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).<\/p>\n

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 Challenge 1: Now suppose that I have 1,000 bitcoins\u00b9. How many ways of distributing them among the two wallets are there?<\/p>\n

 Now suppose that, for security reasons, I don\u2019t want to keep more than 800 bitcoins in a single wallet.<\/p>\n

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 Challenge 2: How many ways of distributing those 1,000 bitcoins are there now?<\/p>\n

Now suppose we add a 3rd wallet and I have no capacity restrictions. Remember that keeping some wallets empty is legal.<\/p>\n

Challenge 3: How many ways of distributing those 1,000 bitcoins among the 3 wallets are there?<\/p>\n

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Let\u2019s add a capacity restriction of 800 bitcoins per wallet once again.<\/p>\n

Challenge 4: How many ways of distributing those 1,000 bitcoins among the 3 wallets are there now?<\/p>\n

Now for those that have cheated by using a computer to solve the previous challenges\u2026<\/p>\n

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

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.<\/p>\n

Challenge 6: How many ways of distributing those 21 million bitcoins among the 3 wallets are there now?<\/p>\n

And finally, let\u2019s add a fourth wallet and remove the capacity restrictions.<\/p>\n

Challenge 7: How many ways of distributing those 21 million bitcoins among the 4 wallets are there now?<\/p>\n

Please post your answers in my forum:<\/p>\n

http:\/\/nestorgames.freeforums.org\/bitcoin-magazine-puzzles-f16.html<\/a><\/p>\n

… and I will reward the best post with a copy of one of my games. I\u2019m looking forward to discussing your findings. Thank you for reading and for your donations! <\/p>\n

You might also enjoy my previous posts:<\/p>\n