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Question 966861: Could you please help me answer this word problem: I am a three digit number. Two of my digits are cubes; and the other is a square.All of my digits are different and are arranged in order from smallest on the left to largest on the right. The sum of my digits is less than fifteen and their product is greater than ten. what number am I
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I am a three digit number.
Two of my digits are cubes; and the other is a square.
All of my digits are different and are arranged in order from smallest on the left to largest on the right.
The sum of my digits is less than fifteen and their product is greater than ten. what number am I
:
You can reason this out.
Only two single digit cubes exist. 1 and 8
Only three single digit squares. 1, 4, 9, since the sum is less than 15, that leaves out 9. All digits are different, leaves out 1
Only the number 1 4 8 would work
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 1 + 4 + 8 = 13
1 * 4 * 8 = 32
1 is equal to 1^3.
4 is equal to 2^2.
8 is equal to 2^3.
each digit is different and they are ordered from smallest to largest.
the sum is less than 15.
the product is greater than 10.
they look like they'll do.
the number is 148.
one of the digits can't be 0 because 0 * anything is equal to 0 which is not greater than 10.
looking at cubes, you can get:
1^3 = 1
2^3 = 8
3^3 = 27.
the cubed numbers can't be greater than 1 or 8, so those have to be your possible cubed numbers.
looking at squares, you can get:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
the squared number can't be greater than 1 or 4 or 9, so those have to be your possible squared numbers.
since all numbers have to be different, and the cubed numbers are 1 and 8, then the squared number can only be 4 or 9.
if the squared number is 9, then 1 + 8 + 9 = 18 which is greater than 15, so the squared number can't be 9.
when the squared number is 4, then 1 + 4 + 8 = 13 which is less than 15, so the squared number can be 4.\
putting the number in ascending order from left to right, you get:
148
1 and 8 are the cubed numbers.
4 is the squared number.
1^3 = 1
2^2 = 4
2^3 = 8
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