# Math Help - 6sided dice

1. ## 6sided dice

You have three 6sided dice.
If you roll the 3 of them, all possible
combos from 1 to 216 are possible.

Of course, the faces are not numbered 1 to 6,
plus some faces will have negative values;
like combo=10 could be 20,30,-40.

Highest face number is 74.

What are the numbers on each dice?

YES...I have the solution!!

2. I count 15 valid solutions. I will post two of them:

Spoiler:

Solution 1

Die 1:
$(70, 69, 68, 67, 66, 65)$

Die 2:
$(72, 66, 60, 54, 48, 42)$

Die 3:
$(74, 38, 2, -34, -70, -106)$

Solution 2

Die 1:
$(74, 73, 72, 71, 70, 69)$

Die 2:
$(72, 66, 60, 54, 48, 42)$

Die 3:
$(70, 34, -2, -38, -74, -110)$

3. Nice.
With this: "Highest face number is 74", I meant |74|; sorry, I wasn't clear.

But if you found 15, you must have that one...

4. Originally Posted by Wilmer
Nice.
With this: "Highest face number is 74", I meant |74|; sorry, I wasn't clear.

But if you found 15, you must have that one...
Actually, none of the 15 solutions I found satisfies that condition. They all have a negative face whose absolute value is greater than 74. In fact, the best I can do is -106.

5. Here tizz:
Spoiler:

74,70,2,-2,-70,-74
73,71,49,47,25,23
69,68,61,60,53,52

6. There are six more solutions, here's the two extreme ones:

Spoiler:

First Extreme

Die 1
$(74, 70, 2, -2, -70, -74)$

Die 2
$(74, 72, 50, 48, 26, 24)$

Die 3
$(68, 67, 60, 59, 52, 51)$

Second Extreme

Die 1
$(74, 70, 2, -2, -70, -74)$

Die 2
$(68, 66, 44, 42, 20, 18)$

Die 3
$(74, 73, 66, 65, 58, 57)$