A six digit number (base 10) is squarish if it satisfies the following conditions:

Level 2

(i) none of its digits are zero; (ii) it is a perfect square; and (iii) the first of two digits, the middle two digits and the last two digits of the number are all perfect squares when considered as two digit numbers.

How many squarish numbers are there?

The answer is 2.

1 solution

X X
Jul 28, 2018

$408^2=166464,804^2=646416$

how do you get these two numbers?

Bulbuul Dev - 2 years, 10 months ago

I suppose that the number should be $\overline{a0b}^2$ ,so it equals $10000a^2+200ab+b^2$ ,so the thing I have to do is to make $2ab$ a perfect square.

X X - 2 years, 10 months ago

A six digit number (base 10) is squarish if it satisfies the following conditions:

The answer is 2.

1 solution

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