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

The Bitcoin Field Puzzle


         The Bitcoin Field Puzzle

Time for another brain burner!

This puzzle is based on my game Tau (2011). TAU was evolved from another game of mine called OMEGA (2010) as a tool to help me teach my students how to multiply in binary base. It exploits a mechanic called ‘multiplicative scoring’.

Let’s start by drawing a square grid of any size (10x10, for example) and filling it with coins, one on each cell. This is our bitcoin field.

FIGURE 1: a 10x10 bitcoin field

Now let’s split the field in two, by drawing a horizontal line like this:

FIGURE 2: two groups

Two groups of coins (above and below the line) have been created. In order to calculate our score, we multiply the number of coins of each group: S = 30 x 70 = 2.100 points.

Now let’s draw a vertical line like this:

FIGURE 3: four groups

 Notice that now there are 4 groups. The new score is: S = 12 x 18 x 28 x 42 = 254.016.

By drawing this second line, we’ve managed to increase the score significantly. If we keep on drawing lines (creating groups) the score will keep on increasing for a while, but if we draw too many lines, it will start dropping!

In fact, if we draw all possible lines, the score will drop to 1 (100 groups of size 1 each)!

FIGURE 4 : 100 groups

Notice also that drawing no lines produces a score of 100.

If a set of horizontal and/or vertical lines produces the highest possible score, this set is called a ‘solution’.

Challenge 1: Find a solution for a 10x10 field.

Challenge 2: Find a solution for a 1.000.000 x 1.000.000 field. Describe it instead of drawing it!

Let’s introduce an interesting twist now. What if some of the cells were empty?

FIGURE 5: field with some empty cells

Challenge 3: Find a solution for the field in figure 5. Empty groups have a value of zero!

And another twist: let’s mix bitcoins and dollars.

FIGURE 6: bitcoins and dollars

In this case, we define ‘solution’ as the partition that produces the highest possible bitcoin score and the lowest possible dollar score.

Challenge 4: Does a solution exist for the field in figure 6? If it does, can you find it?

Challenge 5: Find a partition for the field in figure 6 so that both the bitcoin and dollar scores are maximum.

Please post your answers in the comments section or here:

... 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!


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