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36 Sums, Blank Dice

Date: 03/15/2001 at 02:04:22
From: Kim 
Subject: 36 sums - blank dice


I was given this situation: You have two blank, six-sided dice, and 
you can put any numbers on them. The 12 numbers you choose should be 
able to allow you to make the sums from 1-36.

I got a solution that allowed me to make sums from 0-35 that looks 
like this:

Die 1 has 0, 1, 12, 13, 24, and 25
Die 2 has 0, 2, 4, 6, 8, and 10

I just can't see a way to choose other numbers to be able to make sums 
from 1 to 36.

Thank you in advance if you can help me,
Kim Probst

Date: 03/15/2001 at 12:49:38
From: Doctor Twe
Subject: Re: 36 sums - blank dice

Hi Kim - thanks for writing to Dr. Math.

There are several ways to get the sums 1-36. You already have a pair 
of dice that generate sums 0-35, so how can you get each total to be 
1 more than it currently is? Here's a hint: what would you do to one 
"standard" die to get the totals 2-7 instead of 1-6?

An alternate way of approaching this problem is to think about our 
number system. For two-digit values, we have two digits (like two 
dice), and we get all the numbers from 00 through 99. How do we do 
that? Now think about base 6 instead of base 10...

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum   
Associated Topics:
High School Number Theory
High School Puzzles

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