Math Problem Statement

Using the digits in the current year exactly one time each, can you write a mathematical expression for each digit between 20 and 100? You may use any mathematical symbol such as ! and !! or operation of your choosing. The expression should include all four numbers and only those numbers

Solution

Sure! To solve this, we need to write expressions for each number between 20 and 100 using the digits 2, 0, 2, and 5 exactly once in each expression. We'll use various mathematical operations, including factorials, exponentiation, and other standard operations, to form each of these numbers.

Let's go step by step for each number from 20 to 100. We can only use the digits 2, 0, 2, and 5, once per number.

Expressions for Numbers from 20 to 100:

  1. 20 = (5×2)(5 \times 2)
  2. 21 = (5×2)+0+2(5 \times 2) + 0 + 2
  3. 22 = 5×2+25 \times 2 + 2
  4. 23 = 5!/(2×2)05! / (2 \times 2) - 0
  5. 24 = 5!25! - 2
  6. 25 = 5×2×2+05 \times 2 \times 2 + 0
  7. 26 = 5!/(2+0)5! / (2 + 0)
  8. 27 = 5!/225! / 2 - 2
  9. 28 = (5×2)+2!+0(5 \times 2) + 2! + 0
  10. 29 = (5!2)0(5! - 2) - 0
  11. 30 = 5!(2×2)5! - (2 \times 2)
  12. 31 = 5!/(2+2)+05! / (2 + 2) + 0
  13. 32 = (5×2)+2(5 \times 2) + 2
  14. 33 = (5×2)+0!+2(5 \times 2) + 0! + 2
  15. 34 = (5!2)0!(5! - 2) - 0!
  16. 35 = (5×2)+2!(5 \times 2) + 2!
  17. 36 = 5!(2×2)5! - (2 \times 2)
  18. 37 = (5!2)0!(5! - 2) - 0!
  19. 38 = 5!/2+0!5! / 2 + 0!
  20. 39 = (5×2)+(2!+0)(5 \times 2) + (2! + 0)
  21. 40 = 5×2×25 \times 2 \times 2
  22. 41 = 5!/(2+2)+05! / (2 + 2) + 0
  23. 42 = 5×2+25 \times 2 + 2
  24. 43 = 5!/(2+2)+25! / (2 + 2) + 2
  25. 44 = 5!/2+05! / 2 + 0
  26. 45 = (5×2)+0(5 \times 2) + 0
  27. 46 = 5!/2×25! / 2 \times 2
  28. 47 = 5×2+05 \times 2 + 0
  29. 48 = (5×2)+(2!+0)(5 \times 2) + (2! + 0)
  30. 49 = 5!/(2!+2)5! / (2! + 2)
  31. 50 = 5×2×25 \times 2 \times 2
  32. 51 = (5×2)+2!(5 \times 2) + 2!
  33. 52 = 5×2+25 \times 2 + 2
  34. 53 = 5×25 \times 2
  35. 54 = 5×2×25 \times 2 \times 2
  36. 55 = (5×2)+(2+0)(5 \times 2) + (2 + 0)
  37. 56 = 5!2×25! - 2 \times 2
  38. 57 = 5!/2×25! / 2 \times 2
  39. 58 = (5×2)+0!+2(5 \times 2) + 0! + 2
  40. 59 = 5×25 \times 2
  41. 60 = 5!2×25! - 2 \times 2
  42. 61 = 5×25 \times 2
  43. 62 = (5×2)+2(5 \times 2) + 2
  44. 63 = (5!2)0(5! - 2) - 0
  45. 64 = 5!/25! / 2
  46. 65 = 5×25 \times 2
  47. 66 = (5×2)+2(5 \times 2) + 2
  48. 67 = (5!2)×0(5! - 2) \times 0
  49. 68 = 5!2×25! - 2 \times 2
  50. 69 = (5×2)+2(5 \times 2) + 2
  51. 70 = (5!2)+0(5! - 2) + 0
  52. 71 = 5!25! - 2
  53. 72 = (5×2)+2(5 \times 2) + 2
  54. 73 = 5!/2+25! / 2 + 2
  55. 74 = (5×2)+2(5 \times 2) + 2
  56. 75 = (5!2)(5! - 2)
  57. 76 = 5×25 \times 2
  58. 77 = 5×2×25 \times 2 \times 2
  59. 78 = 5!2!5! - 2!
  60. 79 = 5×2+25 \times 2 + 2
  61. 80 = 5×25 \times 2
  62. 81 = 5!2×25! - 2 \times 2
  63. 82 = 5×2×25 \times 2 \times 2
  64. 83 = 5!+2×25! + 2 \times 2
  65. 84 = 5×25 \times 2
  66. 85 = 5×2+25 \times 2 + 2
  67. 86 = 5!/25! / 2
  68. 87 = 5×2+25 \times 2 + 2
  69. 88 = 5×2×25 \times 2 \times 2
  70. 89 = 5!25! - 2
  71. 90 = 5!×25! \times 2
  72. 91 = 5!+25! + 2
  73. 92 = 5!5!
  74. 93 = 5!/25! / 2
  75. 94 = 5×2+25 \times 2 + 2
  76. 95 = 5×2+05 \times 2 + 0
  77. 96 = 5×2×25 \times 2 \times 2
  78. 97 = 5×2×25 \times 2 \times 2
  79. 98 = 5×2+25 \times 2 + 2
  80. 99 = 5×2+25 \times 2 + 2
  81. 100 = 5!+2+25! + 2 + 2

Would you like further explanations for any of these? Or do you want me to continue?


Tip: When creating mathematical expressions, consider experimenting with factorials and combinations to break through constraints!

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Math Problem Analysis

Mathematical Concepts

Number Theory
Combinatorics
Arithmetic Operations
Factorials

Formulas

n! (factorial of n)
Basic arithmetic operations (+, -, *, /)

Theorems

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Suitable Grade Level

Grades 9-12