0

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

Bram28
  • 100,612
  • 6
  • 70
  • 118
surya krishna
  • 3
  • Hint: from the formula $(100T+X)(100T+Y) = (10000T^2+200T(X+Y)+XY)$, you should be able to see that there is only one possible value of $T$. – Connor Harris Mar 21 '17 at 18:53
  • $ 100< TWO < 141$ go through these 40 possibilities ... there are only $6$ possibilities that end ** when you square them ... more hints on request. – Donald Splutterwit Mar 21 '17 at 19:00
  • @ConnorHarris (100T+10W+O)(100T+10W+O) , right ??? – surya krishna Mar 21 '17 at 19:06
  • @suryakrishna 100T+X or 100T+10W+O ... it doesn't matter ... just focus on what happens with the T! – Bram28 Mar 21 '17 at 19:09
  • @Bram28 , how come T can take only 1 value. it can take any value from 1-9, right ? – surya krishna Mar 21 '17 at 19:12
  • @suryakrishna No, the result of the multiplication TWO * TWO is THREE, so that starts with the T. .. and has only 4 digits after that. There is only one possible value of T for that to happen. Just try a few values to see for yourself, e.g. 389*389 = 151321 ... too many digits ... so you already know T has to be pretty small ... and how can the first digit end up being the same? Again, there is only 1 possibility for that to happen! – Bram28 Mar 21 '17 at 19:18

2 Answers2

1

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

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

$2W < 10$

$W < 5$ 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.

Doug M
  • 57,877
0

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

Bram28
  • 100,612
  • 6
  • 70
  • 118