Hi, have been lurking here at sciforums for quite a while... all you guys are pretty cool. Well, I'm playing a game and I can't seem to decifer or solve the problem. Thought you guys could help... please? Please Register or Log in to view the hidden image! It's a times table. and it's not in order. Each letter is a number but it's not in chronological order. There are 10 letters. The letters are: A-G-H-K-L-N-S-U-X-Y The problems are: X*U=AK X*S=NH X*G=X X*GY=XY X*H=AG X*GG=XX X*K=LN X*N=UA X*GA=KU X*L=HL X*A=GU X*X=US Can you guys help? Can't seem to get my thinking cap on this one.... It's probably very easy but I just don't get it. btw, the game is all in good fun, no real winners, or prizes or such. It's just for the sake of having fun.
(Technically, you mean to say that each letter represents a DIGIT and they are not in numerical order. Also I am assuming although you did not say it that each letter is a DISTINCT digit.) I don't know that I will be able to do it all just sitting here but one obvious point is that "X*G=X" tells us that G= 1. Then from "X*GY= XY" we know X*1Y= 10X+XY= XY So we must have XY= Y. Since neither X nor Y can be 1 we must have Y= 0 so that X*1Y= X*10= X0. Of course, X*GG= XX just confirms that G= 1: X*11= XX. Looking at "X*L= HL", just try things: L can't be 2 because then it would have to be 6*2= 12 and H can't be 1. L can't be 3 because X*3 doesn't end in a "3" for any X>1. L COULD be 4 because 6*4= 24. L could also be 5 (in which case X cpuld be 7 or 9). I'll let others take it from here. I have to run.
Dammit, I'm supposed to be working Please Register or Log in to view the hidden image! But I couldn't help looking at this. X*G=X, so G =1 And From X*GA=KU and X*A=GU You can get 1) X*1A=KU and 2)X*A =1U NOTE: I am assuming that when you write KU you mean a two digit number, first number K second number U. NOT K times U Please Register or Log in to view the hidden image! 1) is also 10X + X*A = KU Subtract 2) and you get 10X = KU - 1U Now if you look at KU - 1U and think about it, you'll see that it must be (k-1)0 (that is, the first digit is (k-1) and the second digit is zero) Since say, 27 - 17 = 10 (k =2, U= 7) or 49 -19 = 30 (k=4, U=9) Get it? Please Register or Log in to view the hidden image! Therefore you have 10X = (k-1)0 And therefore X = K-1 That's all I have for now G =1 and X = K -1 But it should help you start. Adam
Just to be clear, what he means is: X*GY = XY Therefore X*1Y = 10X + X*Y = XY And that XY can be written as 10X + Y Therefore, 10X +X*Y = 10X + Y And therefor X*Y = Y And, since G =1, therefore Y = 0 It gets hard to read if you leave out the * when you mean multiplication Please Register or Log in to view the hidden image! So you now have X= K - 1 and G = 1 and Y = 0 Adam
Ok, solved the rest Please Register or Log in to view the hidden image! The key, after you know G =1 is this equation. X*H = AG Since G =1, the AG is either 11, 21, 31,..., 91. Out of these, only 21 can be the product of 2 single digit numbers. And those numbers are 3 and 7. And that gives A = 2 Now, either X = 3 or X =7 But we have X*A = GU or X*2 = 1U But 3*2 is only 6, so X must be 7. That gives X=7, G=1, Y=0, A=2, U=4 (from 7*2 = 1U) The rest are easy.... that was fun Please Register or Log in to view the hidden image! Adam
Thank you!! Thank you!! You guys are the best. Please Register or Log in to view the hidden image! And Andre, Questions + Answers = Appreciation. Please Register or Log in to view the hidden image! The answers were easy though I just couldn't see it yesterday... Kudos to everyone. This is very much appreciated. Please Register or Log in to view the hidden image!