ppuzzle.org
A COMPENDIUM OF PUZZLES & ENIGMAS
The Locked Sequence
A cipher presents itself as a sequence of symbols, each derived from its predecessor by a rule that shifts at the seventh position. The solver must first identify the rule, then identify its transformation, then apply the transformed rule to predict the twelfth symbol. Many have attempted this puzzle by brute enumeration; the elegant solution requires recognizing the sequence as a modular composition.
Turn the pageConsider that the seventh position is not a break but a mirror. The rule does not change -- it reflects. Read the sequence backward from position seven and you will find the forward rule encoded in reverse.
The Scholar's Tiles
Five pentagonal tiles, each with a unique edge coloring, must be arranged on a hexagonal grid such that every shared edge matches in color. The constraint space appears enormous, but the boundary conditions reduce it to a single family of solutions. The key insight is that the grid's topology, not its geometry, determines the answer.
Turn the pageBegin with the tile that has the most constrained edge coloring. It can only sit in two positions on the hex grid. From there, the cascade of constraints places each remaining tile uniquely.
The Alchemist's Sum
A medieval alchemist recorded four numbers on a parchment, claiming their product equals their sum. The alchemist further noted that no number exceeds ten and all are distinct positive integers. How many such quadruples exist? The answer illuminates a deep property of multiplicative partitions.
The Warden's Paradox
Three prisoners are told that at least one of them will be released at dawn. Each prisoner asks the warden to name one of the other two who will not be released. The warden complies. Has any prisoner gained information about their own fate? The answer depends on whether the warden's choice was forced or free.