Write a Three-Digit Number

Date: 10/24/2001 at 18:01:32
From: Darlen
Subject: Math

My 3rd grade child needs to solve this problem and I don't know the 
answer. Please help. 

Write a three-digit number using the digits 3, 6, and 9. The hundreds 
digit is the sum of the tens and ones digits. The ones digit is 
greater than the tens digit.

Date: 10/24/2001 at 20:09:57
From: Doctor Sarah
Subject: Re: Math

Hi Darlen - thanks for writing to Dr. Math.

This is a great little puzzle for a third-grader! You have to know 
something about place value, and then you can reason it through 
logically.

To review: in the number 369, 3 is the digit in the hundreds place; 6 
is the digit in the tens place, and 9 is the digit in the ones place.

Let's start by creating a list of all the three-digit numbers we can 
make using the digits 3, 6, and 9 (you might want to have your child 
do this for practice):

 A      B      C
369    639    936
396    693    963

Can you find any more?

Now let's look at the clues and see if any of these numbers fit.

1) The hundreds digit is the sum of the tens and ones digits. 

   That gets rid of the numbers in columns A and B, right? The 
hundreds digit in column A is 3, which is less than 6 and 9; and the 
hundreds digit in column B is 6, which is less than 3 and 9. 

   But both numbers under column C work: 9 is the sum of 3 and 6. So 
we're left with:

     C
    936
    963

2) The ones digit is greater than the tens digit. 

   That gets rid of 963 because the ones digit in 963 is 3, and the 
tens digit is 6, and 3 is not greater than 6. So we're left with:

    936

Does that make sense to you and to your child?

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/