Please help me in solving this Algebraic puzzle.

Question

enter image description here Please help me in solving this algebraic puzzle.

Answer 1

HINT

First figure out the value of T; there is only one possibility just focusing on the T's

After that, there are very few possibilities of W, and also limited possibilities of O (e.g. O can't be 5 or 6 ... and knowing T, that'll rule out more). With that, just try the remaining few options

Answer 2

$(100T^2 + 10 W + O)^2 = 10,000 T^2 + 2000 TW + 100 (W^2 + 2TO) + 20 (WO) + O^2$

$T^2 = T; T = 1.$

$2W < 10$

$W < 5$ and not $1, W \in \{2,3,4\}.$ And $4$ is quite doubtful as it will be so close to be rounding up.

$O \notin \{6,5,0\}$ or $O^2$ would end with $O$

$O \in\{2,3,4,7,8\}$

If the smallest $O$ can be is $2$, looking back at $W, 4$ no longer works.

We are down to $10$ possible values of $TWO.$ Only one of which ends with repeated digits.