On examining the calculations at the top of the puzzle, solvers will note that they do not necessarily follow the rules of binary arithmetic, and subtraction acts upon numbers with leading zeros differently from numbers without. Each operation, however, does follow the rules of some canonical number representation using 1's and 0's. The operations are as follows:
| Addition: Subtraction: Multiplication: Division: Exponentiation: |
Base -1+i (A tutorial can be found here) Fibonacci Coding Base -2 (Negabinary) NegaFibonacci Representation Binary |
Once the number systems have been identified, the calculations at the bottom of the puzzle can be performed. The results are as follows:
((((11111×111) + (110^(1010÷10010)))×((1101×(1011 + 1010)) + (11101×10))) – (((1011 – 0011)^101) + (((11011×1110) + 1)×(10^101)))) + (((11110 + 1100)^1011)÷1010) = 0100001101001111
(((((1010×10100×(1010 + 1011))÷(11×110)) + ((((11101×1111×1111) + 100)×10001)÷(11100 + 1110)))×1111) – (11101×(10111 + (10^101)))) + (1111 + 110) = 0101001001001110
((((((11^100) + 1010)×1001) + (10^110)) – ((11111×((1010^10) + 1001)) + 1000))×(100^100)) + ((((101^11) + 10)×11111×11111×11110×101)÷(11111×10110×(1000 + 1001 + 1000))) = 0100001101000001
(11101×10110) + (((1001 + (10101×1000) + ((((1100 + 100)×(101 + 100 + 100)) + 1010)×11101))×1001) – (((((1001 + 1000 + 1000)×(1011 + 1010))÷10001) + (01011 – 10011))×101)) = 0100101101000101
These are all either 16-bit (with leading zero) or 15-bit numbers; interpreting them as pairs of ASCII characters in the given order yields "CORNCAKE", the answer.