Tuesday, 30 March 2021

Dice.

https://www.youtube.com/watch?v=xHh0ui5mi_E

 

First die:

  • 1: two different numbers with difference of 1 between them (e.g. 1 1 2 or 1 2 2 or 6 6 1 or w/e)  
  • 2: two different numbers with difference of 2 between them (e.g. 1 3 3)  
  • 3: three different numbers with differences 1 -> 1 (e.g. 1 2 3 or 5 6 1)  
  • 4: three different numbers with differences 1 -> 2 (e.g. 1 2 4 or 6 1 3)  
  • 5: three different numbers with differences 2 -> 1 (e.g. 1 3 4 or 5 1 2) 
  • 6: all of the remaining combinations (e.g. 1 1 1 or 1 4 4 or 1 3 5)

Second die:

1) if the first die is 1 to 5, you can easily choose the "first" number in the sequence as your second die - for example from 5 6 1 you will choose 5 because the sequence is with differences 1 and 1. And from 6 1 1 you will choose 6 cause it's a sequence with a difference of 1.
2) if the first die is 6, well, you will have to split the choices:  
  • 1 is 1 4 4 and 1 1 4 
  • 2 is 2 5 5 and 2 2 5 
  • 3 is 3 6 6 and 3 3 6 
  • 4 is 2 4 6 
  • 5 is 1 3 5 
  • 6 is 1 1 1, 2 2 2, 3 3 3, 4 4 4, 5 5 5, 6 6 6 

There might be more elegant solutions but I think the above is fairly easy to remember overall. You need to remember only the combinations with 6 as first die.

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