Here is a collection of short, open-ended, mathematically-based programming challenges. They can typically be solved in no more than 10-lines of code.

1. A series to find $\pi$

2. Show $\sin^2(x)+\cos^2(x)=1$

3. Find the square root of a number.

4. Euler polynomial and primes

5. Sum square different

6. Add the digits of a number

7. Archimedean spiral

8. Recurrence relation

9. Fractions with square root

10. $n$ integer to perfect square

11. Integer terms

12. $n$ divisible by 3

13. Which is larger?

14. Sum equals product

15. x squared

16. Sum of geometric series

17. Sum numbers to find pi

18. Not multiples of 6 or 15

19. Variable quadratic coefficient

20. Slope of a line

21. Fibonacci Sequence

22. Sequence converge

23. Rolling two dice

24. Round to the nearest integer

25. Gaussian Random Numbers

26. Average of sine

27. Average of sine with an offset

28. x and its absolute value

29. Arithmetic Series

30. Rotate a square

31. Iterate the square root

32. Iterate the $\sin(x)$ or $\cos(x)$

33. Sides of a Triangle

34. sin(x)/x as x goes to zero

35. Imaginary root of a quadratic equation

36. Make a Plot

37. Roots of a polynomial

38. What does uniform mean?

39. Funny absolute value = 1

40. Dice rolls larger than 100

41. Solve a quadratic by iteration

42. Random Walk

43. Perfect square

44. Happy Valentine's Day

45. Standard deviation

46. Coin Flips

47. Coin Flips Again

48. Obtuse Triangle

49. Golden Ratio Again

50. Golden Ratio

51. Draw a line

52. Distance in 3D

53. Random number range

54. Recurrence Relation

55. A limit

56. Coincidences

57. Divisible by 11

58. The Collatz conjecture

59. Square Line Picking

60. Fractions of 7

61. 1/89

62. John and Mary's dice roll

63. 5 random numbers

64. Airplane seating

65. Non squares

66. Different birthday problem

67. x-squared and x-cubed

68. Two integers

69. Expected value

70. Prove an inverse tan indentity

71. Find some triples

72. Product of 1/2

73. Perfect cube

74. Maximal value

75. Remainder of a division

76. Random on the number line

77. Five integers

78. Three integers

79. Three dice rolled

80. Three random numbers on [0,n]

81. Twiddle with some numbers

82. Powers of 2 and 3

83. Integers to 2001

84. Integers sum to 15

85. Funny square root

86. Integers a, b, c, and d

87. 49 integers

88. Counting to 2003

89. Factors of 60

90. Numbers and their reciprocals

91. Juggler sequence

92. F.O.I.L. big time

93. Fractional part of 1/x

94. LCM and GCD

95. Reduce a fraction to lowest terms

96. Palindromic Squares

97. Three digit numbers

98. Has 7 as a digit

99. Get a digit

100. Reverse a number

101. Goldbach Conjecture

102. Twin primes

103. Breaking a stick

104. Find some Emirps