________ + ________ = ________
Fill in the blanks with sequential digits to make the sum correct. For example: 4 + 5 = 32. Digits may be combined to make multi-digit numbers or used as exponents.
Source: Based on a puzzle in Barry R. Clarke's Brain Busters.
1+2=3 3^2+5=14 76+5=3^4 178+56=234 381 + 546 = 927 Using the null-digit one can get "true" solutions as e.g.: 63+42=105 but also "cheated" ones. E.g., starting from the "natural" solution: 3^0+1=2 one can build other solutions by replacing the single digit 3 with 34, or 345, or 3456 and so on. Similar cheated examples come from: 3^4+1567^0=82 215+4^0=6^3 0^14567+8=2^3 0^35+16=2^4 0^145678+9=3^2; There is a trivial solution for digits 1-9 in which all digits are in order. 1^(234567)+8=9 You may also accept (01)^(234567)+8=9 if you allow leading zeros. If digits do not need to be in order, any equation including 1 can be extended, for example: (2^3)+(1^456780)=9 if 0 is included, everything can be added easily, for example: 4+5=3^2 --> (4^(16789^0))+5=(3^2) which means any equation which fits the pattern can be extended. Some "important" regular examples are: 342+756=1098 and 423+675=1098 (and relevant permutations) 3^6 + 729 = 1458 3^6 + 549 = 1278 5^4 + 673 = 1298 6^4 + 283 = 1579 Using all 10 digits and no exponents, there are 72 solutions of the type 1978 + 56 = 2034 and 96 of the type 789 + 246 = 1035, counting a lot of trivial variations like switching the addends or switching just the ones digits of the addends. That comes from the alphametic solver here: http://www.tkcs-collins.com/truman/alphamet/alpha_solve.shtml 1 + 2 = 3 1^4 + 2 = 3 1^456789 + 2 = 3 173 + 286 = 459 4 + 2^5 = 36 5^2 + 3^4 = 106 4^3 + 56 = 120