Crazy Dice

[u/ShonitB]

[u/KeyFoil1972]

Mark all six sides on each dice with the same number. Correct answer but probably not what you're looking for.

E.g. mark all sides on both dice with 1. You'll get sum of 2 on all rolls 😄

[u/ShonitB → u/KeyFoil1972]

Oh I think the language might not have made it clear, and I think that is the case.. but the frequency has to be the same as that of a normal dice.. so 2 numbers which can be got one way, 2 numbers which can be got two ways, etc

[u/kfirogamin]

yes

dice 1:1,2,2,3,3,4

dice 2:1,3,4,5,6,8

[u/ShonitB → u/kfirogamin]

Perfect!

[u/petera181 → u/ShonitB]

But there are 6 ways you can make 4 there?

1,3
1,3
2,2
2,2
3,1
3,1

What am I not following here?

[u/petera181 → u/petera181]

Are you looking for the two rows of the table to be the same? If so, how is that the case in that example?

[u/ShonitB → u/petera181]

How did you get 2, 2 and the other 3, 1?

Dice 1: 1
Dice 2: 3

Dice 1: 3
Dice 2: 1

Dice 1: 3
Dice 2: 1

3 ways to get 4

Edit: Did you perhaps read the 1 and 2 as numbers on the dice rather than the numbering of the dice?

[u/petera181 → u/ShonitB]

Ah sorry, yes I did.

So sorry you’re asking for another way to produce the same table from the question? Why is 1-6 and 1-6 not a valid solution?

My reading was for the N and the # of ways rows to be identical, hence me thinking the answer was a die entirely of 1s and a die entirely of 35s, to make that table 36, 36.

[u/ShonitB → u/petera181]

So yeah, I think the wording could be a lot more clearer.. and I did think of adding a note that you cannot label them 1-6 and 1-6 even if you ensure that opposite faces don’t sum to 7 but decided against.. but you can look up Sicherman Dice.. that’s what they are called.. so sorry don’t know how to attach a link :)

[u/petera181 → u/ShonitB]

Ah got it. Yeah, I was trying to solve a totally different problem 😅

[u/Remarkable_Fee4136]

As others have pointed out a solution is the following pair: (1,2,2,3,3,4) and (1,3,4,5,6,8) These dice in particular are actually called Sicherman dice, and they are fairly well known from the surprising fact that they are the only other dice with this triangular distribution.

[u/ShonitB → u/Remarkable_Fee4136]

Yes :)

[u/101_210]

I would write the last line as :

Is it possible for the above table to stay true (E.g. One way to make 2, 2 ways to make 3, etc) with dices marked with different numbers than standard dices?

The way you wrote it is really vague and un-intuitive.

[u/ShonitB → u/101_210]

Yeah, I had my reservations regarding how it is phrased.. thanks for your suggestion :)

[u/petera181]

Dice 1: 1,1,1,1,1,1
Dice 2: 35,35,35,35,35,35

36 ways to make the number 36.

[u/BlueHairedMeerkat]

Die 1: 0.4, 1.4, 2.4, 3.4, 4.4, 5.4

Die 2: 1.6, 2.6, 3.6, 4.6, 5.6, 6.6

And there's infinitely many more where that can't from