CISRA Puzzle Competition 2007  SolutionsThis is the archive of the 2007 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition. C.2 CalculateIntuitive Leap: "+" and "" refer to adding or subtracting segments of the digits on a calculator 7segment display. Here's the lesson: 0 = (9  4) + (8  3) + 1 1 = (8  2)  (9  3) + (9  5) 2 = (3  1) + (8  5) 3 = (9  4) + (8  0) + 1 4 = (9  3) + (8 = 0) + 1 5 = (3  1) + (8  2) 6 = 8  (9  5) 7 = A  (6  5)  (8  0) 8 = 9 + (6  5) 9 = (8  2) + (8  6) + (3  1) We can rewrite the first equation using the 7 segment display of a cheap calculator like so: _ _ _ _   = ( _  _ ) + ( _  _ ) +  _ _  _ _  Taking the segments of "4" away from the segments of "9" leaves two segments, on the top and the bottom. Likewise, "8"  "3" leaves two vertical segments: _ _   = +  +  _ _  
The other equations can be seen to hold too. The puzzle text draws special attention to the number 7. Let's look at it: _ _ _ _ _ _  = _  ( _  _ )  ( _    )    _ _ _ _ which becomes _ _  = _   _     which becomes _ _  =     which tells us that the digit '7' must have a hanging descender on the topleft of its representation. The homework asks for solutions to several equations: ? = 8  (9  4) ? = 7 + (6  5) + (8  0) ? = (6  5) + (8  0) ? = (8  7) + 1 ? = 0  1 ? = (9  5) + (8  4) + (8  2) ? = 2  (9  4)  (8  6) ? = 8  1 We can now "calculate" the answers to each line: H = 8  (9  4) A = 7 + (6  5) + (8  0) r = (6  5) + (8  0) d = (8  7) + 1 C = 0  1 O = (9  5) + (8  4) + (8  2) r = 2  (9  4)  (8  6) E = 8  1 The answer is revealed as HARDCORE.
