I remember the first time I heard the puzzle: If you’re paid a penny on the first day, doubled on the second day, and doubled every day after, by the end of the month you’d be a millionaire many times over. This concept is mind boggling.
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\nHere’s code I wrote that demonstrates the puzzle:<\/p>\n
\r\n#include <stdio.h>\r\n\r\nint main()\r\n{\r\n int days,d;\r\n float total;\r\n\r\n printf(\"Number of days in the month: \");\r\n scanf(\"%d\",&days);\r\n\r\n total = 0.01;\r\n for(d=1;d<days;d++)\r\n {\r\n total *= 2;\r\n }\r\n printf(\"At the end of %d days, you have $%.2f\\n\",\r\n days,\r\n total\r\n );\r\n\r\n return(0);\r\n}<\/pre>\nThis month has 31 days, so here’s the sample run:<\/p>\n
Number of days in the month: 31
\nAt the end of 31 days, you have $10737418.00<\/code><\/p>\nMathematicians and others with large brains explain that the value obtained is calculated as 2n<\/em>-1<\/sup> where n<\/em> is the number of days in the month.<\/p>\nAnother fun, cumulative math thing is the factorial. This value is calculated as the product of a whole number and all smaller integers down to 1. So 5! (read as “five factorial”) is 5×4×3×2×1 = 120. Calculating a factorial is also possible in C; refer to my 2014 series<\/a> on this topic, which also covers recursion.<\/p>\nOne other cumulative math thingie, without a clever name I’m aware of, is to add the numbers. Yes, it’s far more boring than the penny-a-day puzzle or factorials, but it’s something you can program in C: Take a value, such as 200. If you were to add all the integers from 1 to 200, what would be the result?<\/p>\n
Don’t bother doing the math in your head! Code the puzzle in C: Your task is to write a program with the cumulative()<\/em> function. Prompt the user for positive integer input. Call the cumulative()<\/em> function to return the cumulative total of the value input, n<\/em> + n<\/em>-1 + n<\/em>-2 + n<\/em>-3 all the way down to one.<\/p>\nFurther, to make the program more interesting, make the cumulative()<\/em> function recursive to counterbalance the boring aspect of this Exercise.<\/p>\nClick here<\/a> to view my solution, though please try this Exercise on your own before checking out what I’ve done.<\/p>\n","protected":false},"excerpt":{"rendered":"Many math puzzles explore doubling values. This time, I’m going to be boring and just add them. Continue reading