Work on Recreating Numbers

  1. Crazy Representations of Half a Million Natural Numbers: Part 5 – 460.001 to 500.000
  2. Crazy Representations of Half a Million Natural Numbers: Part 4 – 420.001 to 460.000
  3. Crazy Representations of Half a Million Natural Numbers: Part 3 – 380.001 to 420.000
  4. Crazy Representations of Half a Million Natural Numbers: Part 2 – 340.001 to 380.000
  5. Crazy Representations of Half a Million Natural Numbers: Part 1 – 300.001 to 340.000
  6. Crazy Representations of Natural Numbers From 260001 to 280000 – Revised
  7. Crazy Representations of Natural Numbers From 240001 to 260000 – Revised
  8. Crazy Representations of Natural Numbers From 220001 to 240000 – Revised
  9. Crazy Representations of Natural Numbers From 200001 to 220000 – Revised
  10. Crazy Representations of Natural Numbers From 180001 to 200000 – Revised
  11. Crazy Representations of Natural Numbers From 160001 to 180000 – Revised
  12. Crazy Representations of Natural Numbers From 140001 to 160000 – Revised
  13. Crazy Representations of Natural Numbers From 120001 to 140000 – Revised
  14. Crazy Representations of Natural Numbers From 100001 to 120000 – Revised
  15. Multiple Choice Patterns in Selfie Numbers – II
  16. Multiple Representations of Selfie Numbers – II
  17. Multiple Choice Patterns in Selfie Numbers – I
  18. Crazy Representations of Natural Numbers from 0 to 10000 Using Factorial and Square Root
  19. Crazy Representations of Natural Numbers from 0 to 10000 Using Cubic Function
  20. Crazy Representations of Natural Numbers from 0 to 10000 Using Square Function
  21. Fixed Power Representation of Numbers
  22. Unified Study of Narcissistic Numbers without and with Division
  23. Multiple Representations of Selfie Numbers – I
  24. Pyramid-Type Representations of Natural Numbers from 1001 to 10000
  25. Crazy Representations of Natural Numbers From 280001 to 300000 – Revised
  26. Crazy Representations of Natural Numbers 0 to 10000 Using Triangular Numbers
  27. Crazy Representations of Natural Numbers from 0 to 10000 Using Fibonacci Sequence Values
  28. Patterns in Splitted Selfie Fractions
  29. Single Digit Representations of Natural Numbers From 40001 to 50000
  30. Single Digit Representations of Natural Numbers From 30001 to 40000
  31. Single Digit Representations of Natural Numbers From 20001 to 30000
  32. Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531
  33. Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202
  34. Crazy Running Equality Expressions With Factorial and Square-Root
  35. Crazy Representations of Natural Numbers From 20001 to 40000
  36. Crazy Representations of Natural Numbers From 80001 to 100000
  37. Crazy Representations of Natural Numbers From 60001 to 80000
  38. Crazy Representations of Natural Numbers From 40001 to 60000
  39. Pandigital-Type and Pythagorean Triples Patterns
  40. Patterns in Pythagorean Triples
  41. Factorial-Type Numerical Calender 2021
  42. 3 and 5-Digits Multiple Choice Embedded Palprimes
  43. 4-Digits Prime Numbers in Fixed Digits Repetition Prime Patterns
  44. Prime Numbers in Fixed Digits Repetitions Prime Patterns
  45. Same Digits Embedded Palprimes of Lengths 3, 5 and 7
  46. Patterned Single Digits Representations of Natural Numbers
  47. Patterned Single Letter Representations of Natural Numbers
  48. Fixed and Flexible Powers Narcissistic Numbers with Division
  49. Pyramid-Type Representations of Natural Numbers
  50. Different Digits Equivalent Fractions: Three Digits Numerator
  51. Different Digits Equivalent Fractions: Two Digits Numerator
  52. Different Digits Equivalent Fraction: Single Digit Numerator
  53. Patterned Selfie Fractions
  54. Fibonacci Sequence Type Selfie Numbers with Factorial: Reverse Order of Digits
  55. Fibonacci Sequence Type Selfie Numbers with Factorial: Digit’s Order
  56. Fibonacci Sequence Type Selfie Numbers With Square-Root
  57. Different Digits Selfie Fractions: Five Digits Numerator – Pandigital
  58. Different Digits Selfie Fractions: Four Digits Numerator
  59. Different Digits Selfie Fractions: Two and Three Digits Numerators
  60. Repeated Digits Selfie Fractions: Two and Three Digits Numerators
  61. Square-Root Type Selfie Numbers
  62. Prime Numbers in Prime Numbers Up To 5 Digits
  63. Power-Type Semi-Selfie Numbers and Patterns
  64. Selfie Numbers With Binomial Coefficients, Triangular Numbers and Factorial
  65. Same Digits Equality Expressions: Power and Plus
  66. Selfie Numbers With Binomial Coefficients, Triangular Numbers and Square-Root
  67. Fibonacci Sequence Type Selfie Numbers: Basic Operations
  68. Binomial Coefficients Triangular Type Selfie Numbers: Basic Operations
  69. Triangular-Type Selfie Numbers: Reverse Order of Digits
  70. Triangular-Type Selfie Numbers: Digit’s Order
  71. Pandigital Equivalent Selfie Fractions
  72. Selfie Numbers With Binomial Coefficients and Fibonacci Numbers
  73. Selfie Numbers: Basic Operations
  74. Different Digits Equivalent Fractions – II
  75. Different Digits Equivalent Fractions – I
  76. Selfie Fractions: Addable, Subtractable, Dottable and Potentiable
  77. Selfie Numbers With Binomial Coefficients
  78. Cubic-Type Selfie Numbers
  79. Concatenation-Type Selfie Numbers With Factorial and Square-Root
  80. Factorial-Type Selfie Numbers in Reverse Order of Digits
  81. Factorial-Type Selfie Numbers in Digit’s Order
  82. Amicable Numbers With Patterns in Products and Powers
  83. Magic Squares Type Palprimes of Orders 5×5, 7×7 and 9×9
  84. Quadratic-Type Selfie Numbers
  85. Natural Numbers From 1 to 20000 in Terms of Fibonacci Sequence and Triangular Numbers
  86. Selfie Expressions With Factorial, Fibonacci and Triangular Values
  87. Simultaneous Representations of Selfie Numbers in Terms of Fibonacci and Triangular Numbers
  88. Factorial-Power Selfie Expressions
  89. Same Digits Equalities Expressions
  90. Flexible Powers Narcissistic-Type Numbers
  91. Fibonacci Sequence and Selfie Numbers
  92. Triangular-Type Selfie Numbers
  93. Permutable Powers Selfie Numbers
  94. Multiple Choice Power Expressions
  95. Patterns in Selfie and Semi-Selfie Numbers
  96. Semi-Selfie Numbers
  97. Fixed Digits Repetitions Prime Patterns of Length 6
  98. Fixed Digits Repetitions Prime Patterns of Length 7
  99. Fixed Digits Repetitions Prime Patterns of Lengths 10, 9 and 8
  100. Single Letter Patterned Representations and Fibonacci Sequence Values
  101. Single Letter Representations of Natural Numbers from 1 to 11111
  102. Fraction-Type Single Letter Representations of Natural Numbers From 1 to 11111
  103. Permutable Power Minimum Length Representations of Natural Numbers from 0 to 20000
  104. Single Digit Representations of Natural Numbers From 15001 to 20000
  105. Single Digit Representations of Natural Numbers From 10001 to 15000
  106. Palindromic-Type Pandigital Patterns in Pythagorean Triples
  107. Multiple-Type Patterns and Pythagorean Triples
  108. Patterns in Pythagorean Triples Using Single and Double Variable Procedures
  109. Crazy Representations of Natural Numbers From 11112 to 20000
  110. Palindromic-Type Squared Expressions with Palindromic and Non-Palindromic Sums – I
  111. Palindromic-Type Non-Palindromes – I
  112. Palindromic-Type Palindromes – I
  113. All Digits Flexible Power Representations of Natural Numbers From 30001 to 50000
  114. All Digits Flexible Power Representations of Natural Numbers From 11112 to 30000
  115. Single Digit Representations of Natural Numbers From 5001 to 10000
  116. Single Digit Representations of Natural Numbers From 1 to 5000
  117. Running Expressions with Triangular Numbers – I

Work in Magic Squares

  1. New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 108
  2. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 25
  3. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 24
  4. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 21 to 23
  5. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 17 to 20
  6. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 14 to 16
  7. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 11 to 13
  8. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 7 to 10
  9. Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 3 to 6
  10. Universal and Upside-down Magic Cubes
  11. Magic Cubes Based on Magic Squares
  12. Striped Magic Squares of Order 12 – Revised
  13. Striped Magic Squares of Order 16 – Revised
  14. Striped Magic Squares of Order 18
  15. Different Types of Magic Squares of Order 14 Using Bordered Magic Rectangles
  16. Striped Magic Squares of Even Orders 6, 8, 10, 12 and 14
  17. Different Types of Magic Squares of Orders 6, 8, 10 and 12
  18. Cornered Magic Squares in Construction of Magic Squares of Orders 16, 20, 24 and 28
  19. Different Types of Magic Rectangles in Construction of Magic Squares of Order 34
  20. Different Types of Magic Rectangles in Construction of Magic Squares of Order 30
  21. Different Types of Magic Rectangles in Construction of Magic Squares of Order 26
  22. Different Types of Magic Rectangles in Construction of Magic Squares of Order 22
  23. Different Types of Magic Rectangles in Construction of Magic Squares of Orders 14 and 18
  24. Different Types of Magic Rectangles
  25. A Simplified Procedure to Construct Pandiagonal Magic Squares Multiples of 4
  26. New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 81
  27. New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108
  28. Magic Squares of Order 31
  29. Magic Squares of Order 29
  30. Magic Squares of Order 27
  31. Bordered and Pandiagonal Magic Squares Multiples of 20
  32. Bordered Magic Squares Multiples of 18
  33. Bordered and Pandiagonal Magic Squares Multiples of 16
  34. Bordered Magic Squares Multiples of 14
  35. Bordered and Pandiagonal Magic Squares Multiples of 12
  36. Block-Wise Bordered Magic Squares Multiples of 10
  37. Bordered and Pandiagonal Magic Squares Multiples of 8
  38. Bordered Magic Squares Multiples of Order 6
  39. Bordered Magic Squares Multiples of 17
  40. Bordered Magic Squares Multiples of 19
  41. Bordered Magic Squares Multiples of 15
  42. Bordered Magic Squares Multiples of 13
  43. Bordered Magic Squares Multiples of 11
  44. Bordered Magic Squares Multiples of 9
  45. Bordered and Pandiagonal Magic Squares Multiples of 7
  46. Bordered and Pentagonal Magic Squares Multiples of 5
  47. Magic Squares of Orders 25
  48. Magic Squares of Orders 21 and 23
  49. Magic Squares of Orders 17 and 19
  50. Odd Order Magic Squares: Orders 3 to 15
  51. Multiple Order Bordered Magic Squares
  52. Cornered Magic Squares of Orders 14 to 24
  53. Cornered Magic Squares of Orders 5 to 13
  54. Cornered Magic Squares of Order 6
  55. Two Digits Bordered Magic Squares of Orders 34 and 38
  56. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 3
  57. Two digits Bordered Magic Squares of Orders 36 and 40
  58. Two Digits Bordered Magic Squares of Orders 26 and 30
  59. Two Digits Bordered Magic Squares of Orders 10, 14, 18 and 22
  60. Two Digits Bordered Magic Squares of Orders 28 and 32
  61. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24
  62. 8000+ Magic Squares of Order 22 in Different Styles, Models and Designs
  63. Closed Double-Crossed Bordered Magic Rectangles and Magic Squares of Order 42
  64. Double-cross Bordered Magic Rectangles and Magic Squares of Order 42
  65. Single-Cross Bordered Magic Rectangles and Magic Squares of Order 42
  66. Magic Squares of Order 42 Using Bordered Magic Rectangles: A Systematic Procedure
  67. Double Crossed Bordered Magic Rectangles and Magic Squares of Order 40
  68. Single Crossed Bordered Magic Rectangles and Magic Squares of Order 40
  69. Figured Magic Squares of Order 40 Using Bordered Magic Rectangles: A Systematic Procedure
  70. Figured Magic Squares of Order 38 Using Bordered Magic Rectangles: A Systematic Procedure
  71. Figured Magic Squares of Order 36 Using Bordered Magic Rectangles: A Systematic Procedure
  72. Figured Magic Squares of Order 34 Using Bordered Magic Rectangles: A Systematic Procedure
  73. Figured Magic Squares of Order 32 Using Bordered Magic Rectangles: A Systematic Procedure
  74. Figured Magic Squares of Order 30 Using Bordered Magic Rectangles: A Systematic Procedure
  75. Figured Magic Squares of Order 28 Using Bordered Magic Rectangles: A Systematic Procedure
  76. Figured Magic Squares of Order 26 Using Bordered Magic Rectangles: A Systematic Procedure
  77. Figured Magic Squares of Order 24 Using Bordered Magic Rectangles: A Systematic Procedure
  78. Figured Magic Squares of Order 22 Using Bordered Magic Rectangles: A Systematic Procedure
  79. Figured Magic Squares of Orders 18 and 20 Using Bordered Magic Rectangles: A Systematic Procedure
  80. Figured Magic Squares of Orders 6, 10, 12, 14 and 16 Using Bordered Magic Rectangles: A Systematic Procedure
  81. Different Styles of Magic Squares of Order 20 Using Bordered Magic Rectangles
  82. Different Styles of Magic Squares of Order 18 Using Bordered Magic Rectangles
  83. Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles
  84. Few Examples of Magic Squares of Even Orders 20 to 30 Using Bordered Magic Rectangles
  85. Few Examples of Magic Squares of Even Orders 6 to 18 Using Bordered Magic Rectangles
  86. Magic Rectangles in Construction of Magic and Block Bordered Magic Squares
  87. Different Types of Multiple Style Magic Squares of Order 30
  88. Different Types of Multiple Style Magic Squares of Order 28
  89. Different Types of Multiple Style Magic Squares of Order 32
  90. Multiple Style Different Types of Magic Squares of Order 36
  91. Different Types of Multiple Style Magic Squares of Order 40
  92. Different Types of Magic Squares of Order 32: Part 4
  93. Different Types of Magic Squares of Order 32: Part 3
  94. Different Types of Magic Squares of Order 32: Part 2
  95. Different Types of Magic Squares of Order 32: Part 1
  96. Different Types of Magic Squares: Even Number Orders From 10 to 26
  97. 100-Magic Squares of Order 42 With Numbers 00-99
  98. Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022
  99. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4
  100. Creative Magic Squares: Area Representations With Fraction Numbers Entries
  101. Magic Squares With Perfect Square Sum of Entries: Orders 3 to 47
  102. Minimum Perfect Square Sum Bordered and Block-Wise Bordered Magic Squares: Orders 32 to 47
  103. Minimum Perfect Square Sum Bordered and Block-Wise Bordered Magic Squares: Orders 3 to 31
  104. Magic Squares With Perfect Square Sum of Entries: Orders 3 to 31
  105. Sequential Pythagorean Triples and Perfect Square Sum Magic Squares
  106. Generating Pythagorean Triples and Magic Squares: Orders 3 to 31
  107. Block-Wise and Block-Bordered Magic Squares Generated by Pythagorean Triples: Orders 3 to 47
  108. Creative Magic Squares: Increasing and Decreasing Orders Crazy Representations
  109. Creative Magic Squares: Permutable Base-Power Digits Representations
  110. Creative Magic Squares: Single Letter Representations
  111. Creative Magic Squares: Single Digit Representations
  112. Block-Wise Universal Bimagic and Semi-Bimagic Squares With Digits 1 and 8
  113. Odd Order Multiples Universal Magic Squares With 1 and 8
  114. Bordered and Block-Wise Bordered Magic Squares: Odd Order Multiples
  115. Bordered and Block-Wise Bordered Magic Squares: Even Order Multiples
  116. Fixed Digits Repetitions Prime Patterns for 5-Digits Prime Numbers
  117. Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47
  118. Block-Wise and Block-Bordered Magic and Bimagic Squares With Magic Sums 21, 21^2 and 2021
  119. Fractional and Decimal Type Bordered Magic Squares With Magic Sum 2021
  120. Upside-Down Magic Squares of Orders 128, 126 and 120 With Digits 6 and 9
  121. Universal Magic Squares of Orders 128, 126 and 120 With Digits 2 and 5
  122. Universal Magic Squares of Orders 128, 126 and 120 With Digits 1 and 8
  123. Block-Bordered Magic Squares of Prime and Double Prime Orders – III
  124. Block-Bordered Magic Squares of Prime and Double Prime Numbers – II
  125. Block-Bordered Magic Squares of Prime and Double Prime Numbers – I
  126. Upside-Down Magic Squares of Type 4k, 6k and 12k Using the Digits 6 and 9
  127. Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 1 and 8
  128. Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 2 and 5
  129. Upside-Down Magic and Bimagic Squares of Orders 17 to 32 With Digits 6 and 9
  130. Universal Magic and Bimagic Squares of Orders 17 to 32 With Digits 2 and 5
  131. Universal Magic and Bimagic Squares of Orders 17 to 32 With Digits 1 and 8
  132. 2-Digits Universal and Upside-Down Palindromic Magic and Bimagic Squares: Orders 3 to 16
  133. Universal Palindromic Day and Two Digits Magic Squares
  134. Bordered Magic Squares With Order Square Magic Sums
  135. Fractional and Decimal Type Bordered Magic Squares With Magic Sum 2020
  136. General Sum Symmetric and Positive Entries Nested Magic Squares
  137. Symmetric Properties of Nested Magic Squares
  138. Nested Magic Squares With Perfect Square Sums, Pythagorean Triples, and Borders Differences
  139. Block-Wise Constructions of Magic and Bimagic Squares of Orders 8 to 108
  140. Perfect Square Sum Magic Squares
  141. Block-Wise Magic and Bimagic Squares of Orders 39 to 45
  142. Palindromic, Patterned Magic Sums, Composite, and Colored Patterns in Magic Squares
  143. Block-Wise Magic and Bimagic Squares of Orders 12 to 36
  144. Different Digits Magic Squares and Number Patterns
  145. Representations of Letters and Numbers With Equal Sums Magic Squares of Orders 4 and 6
  146. Block-Wise Unequal Sums Magic Squares
  147. Block-Wise Equal Sums Magic Squares of Orders 3k and 6k
  148. Magic Crosses: Repeated and Non Repeated Entries
  149. Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares
  150. Generating Pythagorean Triples, Patterns, and Magic Squares

Mixed Work

  1. Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729
  2. Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares
  3. Mathematical Aspects of 24 and 2024
  4. Mathematical Representations of the Last Day of the Year 23 Written American Style: 12.31.23 (123123)
  5. 23 and 2023 in Numbers and Patterns
  6. Mathematical Beauty of 2022
  7. 21 Mathematical Highlights for 2021
  8. Geometrical, Numerical, and Symmetrical Representations for the Days of 2020
  9. Factorial-Type Numerical Calendar
  10. 2020 In Numbers: Mathematical Style – Revised
  11. 2019 In Numbers

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