ABCD x 4 = DCBA
Date: 08/22/97 at 05:55:57 From: Denise Subject: Puzzle ABCD x 4 = DCBA. What are the values of A,B,C and D? The values are between 0-9 and each is different. We have been trying for days on paper and have absolutely no idea. Can you please HELP? Thanks so much for your time.
Date: 08/22/97 at 15:05:26 From: Doctor Wilkinson Subject: Re: Puzzle First of all, A cannot be greater than 2, because 4 x 3 = 12, and we would have another digit to the left of the D in the product. A cannot be 0, because we don't write numbers with a 0 on the left. And A cannot be 1, because 4 times anything is even, so we can't get a 1 as the last digit of the product. So A must be 2, and we have 2BCD 4 ---- DCB2 Now looking at the leftmost digit of the product, we see that D must be 8 or 9, and it can't be 9, because 4 X 9 is 36, and we wouldn't get the 2 in the product. So we have 2BC8 4 ---- 8CB2 Now since there's no carry into the leftmost position of the product (otherwise we would have a 9 and not an 8), B must be 0, 1, or 2, and it's not 2, because we've already used 2. It's not 0 either, but I'm going to let you figure out why. Assuming you've figured that out, we have to have B = 1, and you should be able to finish it off from there. (There are only a few possibilities at this point). -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.