ABCDE/4 = EDCBADate: 06/30/2003 at 13:22:35 From: Subject: Big Number Puzzle "It is rumoured that there is a five-digit number that, when it is quartered, gives an answer which is its digits in reverse order." For example, if the number were 54,321 (which it isn't) a quarter would be 12,345 (which it isn't). Date: 06/30/2003 at 21:54:15 From: Doctor Jaffee Subject: Re: Big Number Puzzle Hi Molly, This was a very challenging problem, but once I figured out the system to solve it, I was able to get the answer with hardly any trial and error. Here is what I did. Let's call the number abcde. I wrote down on a paper two equations. First, edcba edcba -------- and second, x 4 4) abcde ---------- abcde Now, a basic rule of arithmetic is that only numbers whose last two digits are evenly divisible by 4 can themselves be divided by 4. In other words, 'de' must be divisible by 4. That tells me that 'a' can't be 0,1,2,3,4,5,6, or 7. If 'a' were 0 then abcde would only be a 4-digit number and if 'a' were one of the other numbers 'e' would have to be 1. But that can't be because 4 can only be divided into even numbers. So 'a' must be 8 or 9, which would make 'e' = 2. Then a couldn't be 9 because 9 x 4 = 36 and that would mean e = 6 and we've already established that e must be 2. In the two equations above, replace each of the four 'a's with 8 and replace each of the 4 'e's with 2. Then continue working both the division problem and the multiplication problem together to figure out what b, d, and c must equal. Give it a try and if you want to check your solution with me or if you have difficulties or other questions write back to me and I'll try to help you some more. Good luck, - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ |
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