Forming Palindromic NumbersDate: 12/04/98 at 09:34:10 From: ANDREJ KECKES Subject: Palindromic Numbers Hello, I'm interested in palindromic numbers. I'm wondering if there is a list that tells which numbers can be made into palindromic sums and how many steps would be required. Could you please write me a list for numbers under 10,000? I'm interested in operations with plus, minus, divide, multiply. For example: 32 + 23 = 55 322 - 223 = 99 21 * 12 = 252 11 / 11 = 1 Date: 12/04/98 at 11:32:54 From: Doctor Rob Subject: Re: Palindromic Numbers I found 1532 examples for plus with at least one summand with four decimal digits, such as 8431 + 1348 = 9779, or 8610 + 168 = 8778, or 8200 + 28 = 8228, or 7020 + 207 = 7227. I found 149 examples with the largest summand with three digits. I found 33 examples with the largest summand with two digits. There are 5 examples with the largest summand with one digit. This is too many to list for you. For a start on the list, please see: http://mathforum.org/dr.math/problems/barnes10.11.html There is a similar profusion for minus. Times is much more tractable, with only seven solutions up to 10000: 0 * 0 = 0 1 * 1 = 1 2 * 2 = 4 3 * 3 = 9 11 * 11 = 121 12 * 21 = 252 22 * 22 = 484 For division, you can take any palindrome and divide it by itself: 1239874789321 : 1239874789321 = 1. Aside from these, I found the following two with numerator and denominator < 10000. 8712 : 2178 = 4 9801 : 1089 = 9 - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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