How to Solve the 3rd Herodiana Puzzle: A Step-by-Step Guide
What is the 3rd Herodiana Puzzle?
The 3rd Herodiana Puzzle is a challenging intellectual puzzle that requires critical thinking, analysis, and problem-solving skills. This puzzle was created by Herodianus, a Greek mathematician, over 2,000 years ago. The 3rd Herodiana Puzzle is part of a series of puzzles known as the "Herodiana Puzzles" or "Greek Puzzles," which aim to test a person’s ability to reason, solve problems, and find patterns.
What is the Aim of the Puzzle?
The main aim of the 3rd Herodiana Puzzle is to find the correct value of the 17th term (A17) in a sequence of 17 terms, given the conditions of the problem. The sequence involves numbers that are related in a specific way, making it essential to grasp the underlying pattern to solve the puzzle.
The 3rd Herodiana Puzzle: A Review of the Conditions
To better understand the 3rd Herodiana Puzzle, let’s review its conditions:
• The starting point: The sequence begins with a term that is equal to 1 + 3 + 5 +… + 17 (the formula for the sum of odd numbers up to n).
• The recursive formula: The 3rd Herodiana Puzzle relies on a recursive formula where each term (A1 to A17) is equal to the sum of 3 preceding terms.
• No specific formula: Unlike most sequences, the 3rd Herodiana Puzzle does not involve a specific formula, making it more difficult to solve.
How to Solve the 3rd Herodiana Puzzle
To solve the 3rd Herodiana Puzzle, follow these step-by-step instructions:
Understanding the Recursive Formula
To grasp the 3rd Herodiana Puzzle, it is crucial to comprehend the recursive formula:
A1 = (A0 + A2)
A2 = (A1 + A3)
A3 = (A2 + A4)
…
AN = (AN-1 + AN+1)
In this formula, each term is the sum of two preceding terms. Understand this formula well, as it is essential to the puzzle’s solution.
Analyzing the Starting Point and Building the Sequence
To build the sequence, start by identifying the first term (A0):
A0 = 1 + 3 + 5 +… + 17
You can use a calculator or manually compute the sum:
A0 = 81
Now, apply the recursive formula to determine the first few terms of the sequence:
A1 = (81 + 83) = 164
A2 = (164 + 165) = 329
Continue this process until you reach the desired 17th term (A17). In the process, make sure to keep the calculator handy or double-check calculations to ensure accuracy.
Arriving at the Solution
Apply the recursive formula until you calculate the 17th term (A17).
A16 = (A15 + 418)
A17 = (A16 + A15)
By now, you should be familiar with the sequence values:
A1 = 164, A2 = 329,…, A14 = 2423, A15 = 2564, A16 = 2595, A17 = 2589.