Headscratch Letter Puzzle
Date: 01/25/2002 at 10:34:21 From: Ting Zi Subject: Headscratch! Dear Sir/Madam, I am stuck on this maths problem. Here is the question: Headscratch! You can only use the numbers 0 to 9 for each letter once. G*B=HA D*E=E I*C=C H*A=DE F*J=GJ *=TIMES Can you please explain how to do this problem? Ting Zi
Date: 01/25/2002 at 17:01:13 From: Doctor Peterson Subject: Re: Headscratch! Hi, Ting. Could you show me what ideas you had? You may have been close to an answer and only made some little mistakes, or you may not have been trying the right approach. This takes a little thinking, and I want to give you only the hints you need so you can have the experience of finding the answer yourself. The first things I notice are D*E=E I*C=C There are only two ways that a number can be multiplied by another number and be left unchanged: either the multiplier is 1, or the number that stays the same is 0. So there are two possibilities: D=1, C=0, so 1*E=E and I*0=0 I=1, E=0, so D*0=0 and 1*C=C You can try each of these possibilities and see what happens as you continue thinking. When you determine whether there is any solution making one assumption, switch to the other assumption and try again. You can also look at F*J=GJ and make a list of all possible products of this form. You can ignore any for which any of the digits are 0 or 1, or where two other than the J's are the same (such as 6*2=12). This will leave only four possibilities, I believe, which determine the choices for G. Then look at G*B=HA H*A=DE You will have chosen a value for D or E, so you can find all possibilities for H*A, and then see which can be factored to give G*B. If you need more than these hints, write back and show your thinking as far as you get, so I can help where you really need help. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.