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Todo list: 1. Mastermind With a code of only 4 long, it is possible to guess the correct answer in 5 guesses or less. See. “Computer as Master Mind” by Donald Knuth in J. Rec. Math vol 9(1) 1976-7. Might be able to do it by maintaining an array of possible guesses and prune it ourselves without his complex logic, but I’m not sure... (Quite complex and may be a linked list exercise as well. Best done as a major project methinks.) 2. Triangle numbers: nth number = n(n+1)/2 x n = e(n ln x) 3. Digits of a Number a. find sum of digits b. determine the number of digits in a number c. find the digital root of a number (repeatedly find the sum of the digits until you get a number 0 to 9. Eg: 285: 2+8+5=15: 1+5=6) d. print the digits in reverse order e. find the product of the digits of a number e. find the digital product of a number (product of all non-zero digits of the number.) f. find the persistence of a number. It is the number if times you can multiple the digits iteratively) before you get a single digit number. Eg the persistence of 467 is 4 because 4*6*7=168 1*6*8 = 48 4*8 = 32 3*2 = 6. 4 steps. The persistence of 5 is 0. g. given a number ending with a 6, called A. Let B be A with the 6 moved to the front. Eg A = 4576, then B = 6457. Find all the numbers A (or the first number A), such that B = 4*A. 4. Long division Calculate x/y with only integers to a given number of decimal places or when it terminates: q = x div y print q, “.” r = x mod y while r not= 0 d = r * 10 q = d div y print q r = d mod y 5. Calculate pi using random numbers (Monte Carlo Algorithm) Generate a series of n random numbers, x and y, between 0 and 1. For each pair (x,y), calculate the distance from (0,0). If distance < 1, add 1 to a counter. Then pi . (counter/n)*4 14. 6. Hailstone numbers For a given n, iterate using the following rule: if n is even n = n/2, else n = 3n + 1 Stop after the sequence 4, 2, 1 occurs. Will all n lead to this sequence? Calculate the length of the sequence for a g 7. Poison penny (a very simple version of Nim) x pennies are laid out (x > 3). Two players alternate taking 1 or 2 pennies. Whoever takes the last penny loses. (There can be two players or one player versus the computer.) 8. Simple heads/tails guessing game. Ask the user to guess what the result of the next flip of a coin is. Keep score. Another version is to play even or odd (ie. 2 heads/2 tails or 1 head and 1 tail), the user could flip a coin and so could the computer and either the user or computer could guess the outcome. 33. 9. Paper/Rock/Scissors game Computer and user choose one of the three and compare: paper covers rock rock breaks scissors scissors cuts paper 10. Geometric Formulas: a. Rectangle: i. area = hw ii. perimeter = 2h + 2w b. Parallelogram: i. area= bh ii. perimeter = 2h + 2w c. Triangle: i. area = ½bh ii. Hero’s formula: area = sqrt(s(s-a)(s-b)(s-c)) s=½(a+b+c) iii. perimeter = a + b + c d. Trapezoid: i. area = ½h(a+b) e. Regular polygon: i. area = ¼nb2 cos(PI/n)/sin(PI/n) ii. perimeter = nb f. Circle: i. area = PIr 2 ii. circumference = 2PIr iii. arc length = rt (in radians) g. Box: i. Volume = lwh ii. Surface area = 2(lw + lh + hw) h. Sphere: i. Volume = 4/3PIr 3 ii. Surface Area = 4PIr 2 i. Cylinder: i. Volume = PIr2 h ii. Surface Area = 2PIrh j. Cone: k. Volume = aPIr 2h i. Surface Area = PIrl ii. l=sqrt(r2+h2 ) l.