Earlier today, I presented you with a set of intriguing challenges from the Mathigon puzzle advent calendar. Now, I am delighted to share with you the solutions to these mind-boggling puzzles. So let’s dive in and unravel the mysteries together.
1. The knights are drawing in: In this enigmatic conundrum, we were faced with a scenario involving knights. The objective was to determine how many knights can gather on a chessboard without attacking each other. After careful deliberation, the solution unfolds as follows:
To maximize the number of knights, we need to position them in such a way that no two knights threaten each other. By placing the first knight anywhere on the board, we limit the available spaces for subsequent knights. The pattern arises when we observe that each knight occupies a square that is not attacked by any other knight already placed.
By following this pattern, we realize that the maximum number of knights attainable is equal to half the total number of squares on the chessboard. Therefore, on a standard 8×8 chessboard, the answer would be 32 knights.
Now that we have cracked the first puzzle, let’s move on to the next challenge.
2. The elusive coin flip: In this curious riddle, we were tasked with predicting the outcome of a series of coin flips. The twist was that the flips were performed by a mischievous leprechaun who had an uncanny knack for trickery. To outsmart him, we needed to decipher the underlying pattern and identify the most likely outcome.
Upon careful examination, we discovered that the sequence of flips followed a familiar pattern known as a “Fibonacci word.” This sequence is derived from the Fibonacci sequence, where each term is obtained by concatenating the previous two terms. By applying this principle to the series of coin flips, we can determine the most probable outcome.
For example, if the first three coin flips are heads, tails, tails, we can continue the sequence by appending the previous two outcomes, resulting in the pattern: heads, tails, tails, tails, heads. This pattern will repeat indefinitely as long as we keep extending it.
Now armed with this knowledge, we can predict the future coin flips by simply continuing the Fibonacci word sequence. By doing so, we can impressively outwit the leprechaun and confidently anticipate the outcome of subsequent flips.
With these two mind-bending puzzles now solved, we have exercised our logical thinking and mathematical prowess. Whether it be strategically placing knights on a chessboard or predicting coin flips using the Fibonacci word sequence, these puzzles challenge our intellect, expand our problem-solving skills, and provide a fun and engaging experience.
Stay tuned for more exciting challenges and solutions as we continue to explore the captivating world of mathematics and puzzles.
