Puzzles

https://www.youtube.com/watch?v=_pP_C7HEy3g

On the door there is a “keypad” with magical circles. The players notice they can “move” these circles around.

2	3	4	7	13	16
19	23	29	30	31	36
37	40	41	43	49	53
55	59	61	62	67	71
73	75	79	81	83	89
91	94	97	101	103	107

Clues and Interpretation

• Prime Numbers: The players recognize that some of the numbers in the grid are prime. They need to focus on these prime numbers to solve the puzzle.

• “Perfect Pairs”: The riddle hints that they need to find pairs of prime numbers within the grid that sum up to other primes. They need to determine which pairs are valid.

• 4-Digit Code: The sum of the “perfect pairs” will provide the numbers for the 4-digit code.

Solution Process

1. Identify the Prime Numbers:

   • The players should first identify all prime numbers in the grid: 2, 3, 7, 13, 19, 23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107.

2. Find “Perfect Pairs”:

   • The players need to identify pairs of primes in the grid that sum to another prime number. For example:
     • 2 + 3 = 5 (not in grid, so not valid)
     • 19 + 23 = 42 (not prime, so not valid)
     • 19 + 13 = 32 (not prime, so not valid)
     • 23 + 53 = 76 (not prime, so not valid)
     • 37 + 41 = 78 (not prime, so not valid)
     • 31 + 43 = 74 (not prime, so not valid)
     • 2 + 61 = 63 (not prime, so not valid)
     • But:
       • 19 + 83 = 102 (prime pair that sums to 102)
       • 59 + 13 = 72 (prime pair that sums to 72)
       • 2 + 71 = 73 (prime pair that sums to 73)
       • 31 + 37 = 68 (prime pair that sums to 68)

3. Derive the Code:

   • After identifying several “perfect pairs”, they are now instructed to sum these numbers, or, alternatively, to look for prime pairs where the sums match another prime pair number on the keypad as a reference.

   • Once the players have identified four valid sums, the players should add these sums up to get the final code. For example, if pairs yielding prime sums are 13, 37, 67, and 31, the solution might also be based on how they identify primes of their output:

     They might arrive at: (19+83), (2+71), (13+67), (19+61).

4. Calculate the Final Code:

   • Take those valid numbers, sum up the primes of those pairs, and, from that, they can see the formula is 197 + 61 + 73 + 41 = 372, their final code to unlocking the door.

Hint Options

If the players struggle:

• “Consider each pairing carefully; sometimes a path isn’t just straight but mathematical.”
• “Your final key doesn’t merely lie in adding, but finding the prime sum in each part.”

Final Outcome

After entering the correct code, the magical lock disengages with a resonant chime, and the massive door creaks open, leading the players further into the wizard’s mindscape.

This puzzle adds layers of complexity that should be challenging yet rewarding for players familiar with mathematical concepts, offering them a satisfying experience when they crack the code.