# More Self-Answering Questions

## More Self-answering Questions submitted by readers like you!

Self-answering problems contain their own answers. The winners from the September 2005 contest can be read here. In case that isn't enough, here are more questions submitted by our readers. The answers are highlighted in green. They presented in the order received. If you have your own questions to add, please e-mail them to jquinn@awm-math.org.

1. Express, in Roman numerals, the number before FIVE. (Head-Royce School Math Club in Oakland, CA)

2. Express, in binary, the number of different ways one can answer a 100 question true/false test.  You are not allowed to look it up on Google!  (Head-Royce School Math Club in Oakland, CA)

3. Determine  lim (n®∞) (1+1/n)n(Head-Royce School Math Club in Oakland, CA)

4. At time t=0, water begins pouring into an empty sink so that the volume of water is changing at a rate V'(t)=cos t. For time t=k, where 0< k < π/2, determine the amount of water in the sink. (Raymond Greenwell, Hofstra University)

5. The cost of a widget varies according to the formula C'(t)=-sin t. At time t=0, the cost is \$1. For arbitrary time t, determine a formula for the cost. (Raymond Greenwell, Hofstra University)

6. What is the name of the Washington Monument? (Monty Korpe, Virginia Tech)

7. What is the opposite of the second derivative of f(x) = sin (x)? (Rheta Rubenstein, University of Michigan-Dearborn)

8. What is the fourth derivative of f(x) = sin (x)? (Rheta Rubenstein, University of Michigan-Dearborn)

9. What is an equation for the tangent to the identify function at y = 1?. (Rheta Rubenstein, University of Michigan-Dearborn)

10. Besides zero, how many other numbers are additive identities for the reals? (Rheta Rubenstein, University of Michigan-Dearborn)

11. What is the one identity element for multiplication over the reals? (Rheta Rubenstein, University of Michigan-Dearborn)

12. How many factors does 2 have? (Rheta Rubenstein, University of Michigan-Dearborn)

13. How many letters are in the number four? (Rheta Rubenstein, University of Michigan-Dearborn)

14. What is the reciprocal of the reciprocal of 7? (Rheta Rubenstein, University of Michigan-Dearborn)

15. How many lines of symmetry are there in a regular 4-gon? (Rheta Rubenstein, University of Michigan-Dearborn)

16. A fair spinner is 1/2 blue and 1/2 white.  What is the probability that a spin lands in the blue half? (Rheta Rubenstein, University of Michigan-Dearborn)

17. What fraction of the letters in “a third” are vowels? (Rheta Rubenstein, University of Michigan-Dearborn)

18. What fraction of the letters in “fifth” are vowels? (Rheta Rubenstein, University of Michigan-Dearborn)

19. What function is the derivative of the function f(x) =  ex? (Rheta Rubenstein, University of Michigan-Dearborn)

20. What is the slope of the line y = 0? (Rheta Rubenstein, University of Michigan-Dearborn)

21. What is the perimeter of a unit regular 4-gon? (Rheta Rubenstein, University of Michigan-Dearborn)

22. Describe the relationship among the ls in “parallel.” (Rheta Rubenstein, University of Michigan-Dearborn)

23. What do you do to the length of an edge of a square to find its area? (Rheta Rubenstein, University of Michigan-Dearborn)

24. How many digits in 4444 are four? (Rheta Rubenstein, University of Michigan-Dearborn)

25. Share your reflection about the relationship of a figure to itself if it has one line of symmetry. (Rheta Rubenstein, University of Michigan-Dearborn)

26. What fraction of the letters in “two-thirds” are in “thirds?” (Rheta Rubenstein, University of Michigan-Dearborn)

27. What is one more than the reciprocal of F? (Rheta Rubenstein, University of Michigan-Dearborn)

28. What is the square of the square root of 23? (Rheta Rubenstein, University of Michigan-Dearborn)

29. What statistical measure tells you how far the values in a data set range? (Rheta Rubenstein, University of Michigan-Dearborn)

30. A quarter is what fraction of a dollar? (Rheta Rubenstein, University of Michigan-Dearborn)

31. A fifth is what fraction of a gallon? (Rheta Rubenstein, University of Michigan-Dearborn)

32. What type of angle is made by the first letter of ACUTE? (Rheta Rubenstein, University of Michigan-Dearborn)

33. What is the shape of the last letter in arc? (Rheta Rubenstein, University of Michigan-Dearborn)

34. What is the product when two numbers are multiplied?(Rheta Rubenstein, University of Michigan-Dearborn)

35. How would you describe the double “r” in recurring? (Rheta Rubenstein, University of Michigan-Dearborn)

36. What type of angle is made by the last letter in “right?” (Rheta Rubenstein, University of Michigan-Dearborn)

37. What is the standard way to pronounce “standard?” (Rheta Rubenstein, University of Michigan-Dearborn)

38. What do you call the base of the first letter in the word “vertex?” (Rheta Rubenstein, University of Michigan-Dearborn)

39. What part of a king’s body was first used to define the measure known as a “foot?” (Rheta Rubenstein, University of Michigan-Dearborn)

40. What is the output of the identity function when the input is 36? (Rheta Rubenstein, University of Michigan-Dearborn)

41. Some mathematical symbol produces surprisingly large outputs for relatively small inputs What is it? (Rheta Rubenstein, University of Michigan-Dearborn)

42. How many times would you expect to roll a fair die in order to obtain a "6" for the first time?  (Roger Nelsen, Lewis & Clark College)

43. Find the area of a square with perimeter equal to 16. (Roger Nelsen, Lewis & Clark College)

44. Find the volume of a cube whose surface area is 216. (Roger Nelsen, Lewis & Clark College)

45. Find the perimeter of an equilateral triangle whose area is equal to 12√ 3. (Roger Nelsen, Lewis & Clark College)

46. (Roger Nelsen, Lewis & Clark College)

47. What is the only prime number divisible by 15,485,863? (Gregory Hartman, Virginia Military Institute)

48. Give 1 of the 2 roots of x^2 - 3x + 2. [Or Give 1 of the 2 roots of x^2 - 3x + 2.] (Gregory Hartman, Virginia Military Institute)

49. Give 1, 4 digit prime number that ends with 27. (Gregory Hartman, Virginia Military Institute)

50. Find the sum of the factorials of the digits of 145. [145 (= 1! + 4! + 5!)] (Larry Lesser, University of Texas at El Paso)

51. To the tenths place, find the chi-square value that would indicate significant association at the .05 level  from a 2x3 contingency table. [6.0 (which equals 2 x 3)] (Larry Lesser, University of Texas at El Paso)

52. State one integer that is neither prime nor composite. (Larry Lesser, University of Texas at El Paso)

53. Find the smallest natural number no greater than one-thousand that contains the letter a. (Larry Lesser, University of Texas at El Paso)

54. In what kind of units would you express the area of a “square”? (Larry Lesser, University of Texas at El Paso)

55. Find all numbers whose spelling has exactly four letters.  (Larry Lesser, University of Texas at El Paso)

56. What’s the approximate probability of winning the lottery, if we treat it as a zero-sum game? (Larry Lesser, University of Texas at El Paso)

57. From the letter gamma, how many letters do you have to count through the Greek alphabet to reach the letter xi, giving the answer as a Roman numeral. (Larry Lesser, University of Texas at El Paso)

58. Note integer near eight (Larry Lesser, University of Texas at El Paso)

59. I’m a solution to x2 + 1 = 0.  What am i? (Larry Lesser, University of Texas at El Paso)

60. How often are hands shook, if five people all shake hands with everyone? (Dave Ehren, Macalester College)

61.  How many diagonals does a five-sided convex polygon have?  (Dave Ehren, Macalester College)

62. From 185, subtract thirty five times. What do you get?  (Dave Ehren, Macalester College)

63. What's 1! + 4! + 5!? (James Tanton, St. Mark's Institute for Mathematics)

64. What's 4! + 0! + 5! + 8! + 5! ?  (James Tanton, St. Mark's Institute for Mathematics)

65. How many different types of infinity did Cantor discover?  (James Tanton, St. Mark's Institute for Mathematics)

66. In a twelve-hour period, how many times to the minute and the hour hands of a clock align?  (James Tanton, St. Mark's Institute for Mathematics)

67. One to any power equals ...?  (James Tanton, St. Mark's Institute for Mathematics)

68. Two lists: One contains three consecutive positive integers and the other five consecutive positive integers. Their union has six members and their symmetric difference four. The product of the numbers in first list equals the product of the numbers in the second. What are the numbers appearing in the lists? [4,5,6 and 1,2,3,4,5]  (James Tanton, St. Mark's Institute for Mathematics)

69. Sum of the cubes: Find 3^3 + 7^3 + 0^3. (Art Benjamin, Harvey Mudd College)

70. What is the sum of the proper positive factors of six? (or insert your favorite perfect number) (Robert Vallin, Slippery Rock University)