Decimal hacks aren't usually my taste, but perhaps you'll find this trivia fun (inspired by the newest volume of "Winning Ways"...) To address the dismal state of math education, let's engineer a "dismal arithmetic" to be easier than decimal, so no student will be left behind. You'll still operate on pairs of digits, but you don't have to worry about carrying or in fact doing anything harder than comparing. Instead, for each pair of dismal digits, to Add, take the lArger, but to Multiply, take the sMaller That's it! For example: 169 + 248 ------ 269 and 169 x 248 ------ 168 144 + 122 -------- 12468 You can check that these associate, commute and that multiplication distributes over addition: 357 x (169 + 248) = 357 x 269 = 23567 = 13567 + 23457 = (357 x 169) + (357 x 248) Curiously, while 0 is the additive identity, 1 is *not* the multiplicative unity (Quiz: what *is* the unity?). In fact, 1 even has non-unit divisors, eg 1 x 2 = 1! (Quiz: what's the smallest dismal prime?) If we count the number of dismal partitions of n into distinct positive parts not greater than n we get the bizarre sequence 1 1 2 4 8 16 32 64 128 256 1 5 22 92 376 1520 6112 24512 98176 392960 2 22 200 1696... [not yet sloaned--superseeker thinks it might see a generating function, is it hallucinating?] (Quiz: notice that p(12) = 22 = p(21); does p(13) = 92 = p(n) for any other n?) Perhaps some funsters will enjoy developing this dismal enterprise further...