Numb3rs

Number Theory Level 2

How many three-digit perfect squares are there such that the hundreds digit, half the tens digit and the unit digit are in arithmetic progression?

The answer is 2.

1 solution

Joshua Lowrance
Dec 2, 2019

Perfect Squares	The Sequence Formed	Does it work?
$100$	$1,0,0$	No
$121$	$1,1,1$	Yes
$144$	$1,2,4$	No
$169$	$1,3,9$	No
$196$	$1,4.5,6$	No
$225$	$2,1,5$	No
$256$	$2,2.5,6$	No
$289$	$2,4,9$	No
$324$	$3,1,4$	No
$361$	$3,3,1$	No
$400$	$4,0,0$	No
$441$	$4,2,1$	No
$484$	$4,4,4$	Yes
$529$	$5,1,9$	No
$576$	$5,3.5,6$	No
$625$	$6,1,5$	No
$676$	$6,3.5,6$	No
$729$	$7,1,9$	No
$784$	$7,4,4$	No
$841$	$8,2,1$	No
$900$	$9,0,0$	No
$961$	$9,3,1$	No

Only $121$ and $484$ work.