From: utzoo!decvax!harpo!eagle!mhuxt!cbosg!nscs!jpj Newsgroups: net.math Title: Re: puzzle Article-I.D.: nscs.140 Posted: Fri May 28 10:23:20 1982 Received: Sat May 29 06:17:31 1982 Note that the problem is *not* a math problem at all, it is a *string* problem! Given this, you can crank out answers by noticing that if you choose a value for the right-most digit (say 2) and then multiply by 2 mod 10 to get the next digit (keeping track of carries as necessary), when you get to the left-most digit, multiplying it by 2 and comparing it with the digit you started with will tell you if you have a solution. What I have found indicates that there are *no* solutions for less than 18 digits, that the solution at 18 is a string that can be permuted 8 different ways and that you thus find new solutions at every string of length n*18 - each time 8 solutions! These strings were generated on a VAX in under 2 seconds... n now equals 18 105263157894736842 157894736842105263 210526315789473684 263157894736842105 315789473684210526 368421052631578947 421052631578947368 473684210526315789 . . . n now equals 90 105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842 157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263 210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684 263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105 315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526 368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947 421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789 Cheers... Jim Jenal BTL/CB