Sunday, February 15, 2015

2048 vs 2584

who: J1 and J2
Where: online
When: before and during violin lessons

I don't have many games on my phone, but 2048 is there. It nicely fits J2's love of powers of 2, but J1 also really enjoys it. I will admit that I play a lot more than I think I should.

Assuming that you know the game, what do you make of this board:

Hmm, 2 and 8 are familiar, but 1, 3, 13, and 610?!

Searching recently for something related to the Fibonacci sequence, I found 2584, the Fibonacci sequence version of 2048. Thinking about it briefly, you will see why the sequence fits so nicely into this game structure. Of course, this was bound to be a favourite for the younger J's, too.

A bit of compare and contrast

J1 and J2 played back-to-back games, one round each, swapping in between. Then we talked about how the games compared. Because this was interspersed with other activities, J1 and I talked without J2 and then later got J2's opinions, but J1 waited to hear his thoughts before interjecting. Here were some snippets:

  • J0: Which one is harder? 
  • J1/J2: Fibonacci is harder. 
  • J0; what does that mean, "harder"? Is it harder to play each step or harder to keep going in the game?
  • J1/J2: Harder to play each step. For powers of 2, you just match up the number. For Fibonacci, you have to think about which numbers can combine together. 
  • J0: which one do you think is harder to keep going?
  • J1: the Fibonacci one is easier because each number can combine with two others. Like 3 can combine with 2 or 5, 5 can combine with 3 or 8, 8 can combine with 5 or 13, 13 can combine with 8 or 21.
  • ---------------
  • J0: are the games similar in anyway?
  • J2: yes, both are on a 4 x 4 grid
  • J1: yes, both have sliding number tiles that get added together
  • ---------------
  • J1: why do you win when you get 2584?
  • J0: is it the closest Fibonacci number to 2048?
  • J2: no, 1597 is closer
  • J0: Let's see, what power of 2 is 2048?
  • J2: 14
  • J0: is that correct?
  • J2: .... 11
  • J0: is 2584 the 11th Fibonacci number?
  • J2: let's count them
  • <together>: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584. That's 18 (or maybe we should call it 17 for purposes of the game?)
  • J2: Oh, we knew it had to be more than 12 because 144 is the 12th (which is their favourite Fibonacci number right now because it is also 12 squared)

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