M.Mamikon COUNTING FINGERS "Counting Fingers" is an amaizing activity from MCPT course "NUMBER POWER-1" (chapter 'Linear Patterns'). Counting is done "forwards and backwards" on a hand with 5 fingers. Its algorithm has two main features: periodicity and flipping over after the half of each period. Similar algorithm holds for counting on a hand not just with 5 fingers but with any number of fingers on it, say 2, 3, ... , 5, ... 7, ... etc... The following Applet demonstrates this GENERALIZED counting fingers on a hand with any number of fingers you choose. You can also exercise the inverse problem with this program: Enter any Number and find out on which Finger it lands. Click here: Counting Fingers GENERALIZED The algorithm behind the Java-program uses both formulas, for direct and inverse problems. Can you find these formulas for general case of K fingers on the hand? What is the 'repetition' PERIOD in general case of counting with K fingers? EXPLAIN the following PATTERNS for 5 fingers: (check them using the above Applet) Can you create similar patterns? Number 1 lands on Finger 1, so does 1777... with any number of 7s, and so does 9777... with any number of 7s added. 2 lands on Finger 2, so does 2666... with any number of 6s, so does 2424... with any number of repeating 24s, and so does 104 with any number of '0's added to it. 3 lands on Finger 3, so does 3111... with any number of 1s. 7 lands on Finger 3, so does 7111... with any number of 1s, and so does 7555... with any number of 5s. 11 lands on Finger 3, so does 11333... with any number of 3s. 4 lands on Finger 4, so does 4444... with any number of 4s. 6 lands on Finger 4, so does 6222... with any number of 2s. 5 lands on Finger 5, so does 5333... with any number of 3s. 12 lands on Finger 5, so does 12444... with any number of 4s.