Allan Wechsler <acwacw@gmail.com> wrote:
Dan Asimov <dasimov@earthlink.net> wrote:
ELEVEN + TWO = TWELVE + ONE
Dan, this is just an anagram, right? Unless I'm missing something truly devilish, it's arithmetically impossible.
I've confirmed that there is no solution. Since there are only seven distinct letters, I also tried base 7. Then all bases through 40. Still no solution. (Larger bases are very slow to test.) Would one expect there to be a (possibly non-unique) solution in some base, eventually, just by chance? If so, I propose the opposite challenge -- finding an "anti-alphametic," an arrangement that has no solution in any base. Getting back to my original puzzle under this subject line, I'm about halfway through searching the six-four case, ______=____ with interspersed * + - . / So far I've found about 430,000 arrangements with non-unique solutions and 220 with unique solutions. Of those 220, just 2 have negative values: __*_._-_._=_/__-_ and _*_._/_-_/_=_-__._ Of those 220, 13 contain all of * + - . / and 4 contain all of those once and only once. Those 4 are closely related so I'll only give one of them: __*_.___=_/_-_+_ Again, you're to replace the underscores with each of the ten digits once and only once, and there is a unique solution. I'll re-ask my question: Given that I'm never simplifying fractions, and that I cross-multiply them at the end to check for equality, what are the largest numbers that could appear? Am I at risk for integer overflow? For instance _*_.____=__-_/_ has the unique solution 4*2.8750=13-9/6, which yeilds the fractions 115000/10000 and 69/6. Cross-multiplying those fractions to check if they're equal gives 115000*6 = 10000*69 = 690000.