All About The Digits

Algebra Level 3

Let $a$ , $b$ , and $c$ be single-digit numbers and that $a<b<c$ .

$a^{2}b$ is a two-digit number
$a^{3}b^{2}c$ is a three-digit number

Find the product of all the integer solutions. How many digits does the product have?

Try Part 2

The answer is 15.

1 solution

Kaizen Cyrus
May 29, 2019

The integer solutions are:

$a=2, \space b=3, \space c=4$
$a=2, \space b=3, \space c=5$
$a=2, \space b=3, \space c=6$
$a=2, \space b=3, \space c=7$
$a=2, \space b=3, \space c=8$
$a=2, \space b=3, \space c=9$
$a=2, \space b=4, \space c=5$
$a=2, \space b=4, \space c=6$
$a=2, \space b=4, \space c=7$

Getting all the integer solutions, we get $\small 2^{9}×3^{6}×4^{4}×5^{2}×6^{2}×7^{2}×8×9$ to find their product. The product is $303395084697600$ which has $\boxed{15}$ digits.

All About The Digits

The answer is 15.

1 solution

0 pending reports