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Bovine Math Geniuses
Farmer John loves to help the cows further their mathematical skills. He has promised them Hay-flavored ice cream if they can solve various mathematical problems.
He said to Bessie, "Choose a six digit integer, and tell me what it is. Then extract the middle four digits. Square them and discard digits at the top until you have another number six digits or shorter. Tell me the result."
Bessie, a mathematical genius in disguise, chose the six digit number 655554. "Moo: 6 5 5 5 5 4", she said. She then extracted the middle four digits: 5555 and squared them: 30858025. She kept only the bottom six digits: 858025. "Moo: 8 5 8 0 2 5", she replied to FJ.
FJ nodded wisely, acknowledging Bessie's prowess in arithmetic. "Now keep doing that until you encounter a number that repeats a number already seen," he requested.
Bessie decided she'd better create a table to keep everything straight:
Bessie showed her table to FJ who smiled and produced a big dish of delicious hay ice cream. "That's right, Bessie," he praised. "The chain repeats in a loop of four numbers, of which the first encountered was 217600. The loop was detected after nine iterations."
Help the other cows win ice cream treats. Given a six digit number, calculate the total number of iterations to detect a loop, the first looping number encountered, and also the length of the loop.
FJ wondered if Bessie knew all the tricks. He had made a table to help her, but she never asked:
whose results would be: three iterations to detect a loop, looping on 0, and a length of loop equal to 1.
Remember: Your program can use no more than 16MB of memory.
* Line 1: A single six digit integer that is the start of the sequence testing.
* Line 1: Three space-separated integers: the first number of a loop, the length of the loop, and the minimum number of iterations to detect the loop.
217600 4 9
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