My Math Forum DECODING LETTERS

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 October 27th, 2009, 09:06 AM #1 Newbie   Joined: Jul 2008 Posts: 12 Thanks: 0 DECODING LETTERS Can anybody shed some light on this as how to solve it with equations: T W O X T W O ------------- T H R E E
 October 27th, 2009, 10:01 AM #2 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 Re: DECODING LETTERS I assume it is TWO x TWO=THREE where one letter is for one digit. First of all please mark that T = 1 (otherwise two numbers T** x T** would NOT equal T****, I mean first digit would not be identical). Second - THREE is square of TWO. You wanted some light, is it enough? I mean you need to work yourself, it is maths, i.e. DIY
 October 27th, 2009, 12:40 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,095 Thanks: 1905 Assuming different letters represent different digits, and that decimal arithmetic is used, the letter O cannot represent 0, 1, 3, 4, 5, 6, 7, or 9 (since no perfect squares end in 66 or 99), so it must represent 2 or 8, and so E represents 4. It's now fairly easy to determine what digits O and W represent, and hence what digits H and R represent.
 October 27th, 2009, 03:24 PM #4 Senior Member   Joined: Oct 2009 Posts: 105 Thanks: 0 Re: DECODING LETTERS Why not try to rearrange the problem? So instead of TWO * TWO = THREE Try (100T + 10W + 1O)^2. Find out what that equals and group all of your 10000s, 1000s, 100s, 10s, and 1s together. After that, try to match them with (10000T + 1000H + 100R + 10E + E). To start you off, I got 10000T^2 = 10000T, which means T^2 = T. Obviously, T has to equal one. Edit** Actually... T could be 0 also. This would require H to be 0 as well though. I'm getting answers to fit the format, however my problem is I am ending up with either W equaling T or H equaling T. I can't see another way around this! I ended up getting T = 1, W = 1, O = 2, H = 2, R = 5, and E = 4. 112*112 = 12544 and 012*012 = 00144 This works great if T and W can be considered the same number, however they are assigned different letters which is confusing me. If someone could please share the correct answer, it would be much appreciated. I'm actually starting to believe it is impossible based on the formula I have.
 October 28th, 2009, 03:40 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,095 Thanks: 1905 So O is not 2. However, O = 8 works.

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