On the opposite end of the spectrum from mazes, puzzles use rules and logic to create a problem space. While these puzzles use physical layouts to help define the problem, the problem space created looks nothing like the physical space of the problem. I’ve tried to come up with a few unique types of puzzles for my Imagine column, each relying on a different set of solution strategies.

Updated: October 2016. A set of precincts needs to be grouped into districts. Your nefarious task is to gerrymander the districts so that the desired election result is achieved, regardless of which side (yes or no votes) has the majority of votes or precincts. These puzzles will hopefully enlighten solvers on how gerrymandering is achieved from a mathematical perspective, and how incredibly influential district arrangement can be on election results.

Updated: October 2016. When a neuron receives a signal from enough surrounding neurons, the neuron then passes along the message. This is known as the neuron’s activation threshold. In these puzzles, given the set of neurons and their activation states, can you determine how to assign the available neuron activation thresholds?

Complete each story by using words found through connecting letters in a grid (just like in your favorite dice-shaking word-finding game). The tongue-in-cheek stories are meant to add context to help you locate the missing words, although finding as many words as possible from the grid and then filling in the story is another possible solving technique. I’m terrible at word puzzles, so this is the only type I’ve ever tried to make.

Help complete a fish ladder around a dam so that diadromous fish can return upstream to spawn. Using the available pre-cast, stackable columns, build up from the fluctuating height of the river bottom so that the water steps down in gradual, traversable increments.

While driving from start to finish through a city district, you need to follow the rules of an if-then-else statement regarding which direction you turn (or go straight) at certain intersections. These puzzles are meant to help solvers understand the logical structure of if-then-else statements and include multiple if-then-else statements for each city district.

A harmful disease is being transmitted within a small population. Given who is infected, who has come in contact with whom, the time elapsed, and the number of those vaccinated against the disease, can you determine who must have been patient zero?

The very first type of puzzle I ever created (and the first ever published in Imagine), these puzzles consist of a grid of blue blocks. You’ll need to fill each block with one of a selection of stamps, 4x4 colored grids that can be rotated but not reflected (just like a real rubber stamp). The puzzle is solved when the colored squares in each row and column sum to the values given.

You are planning a wind farm on a given piece of land. Each turbine needs space on three sides to separate it from adjacent turbines. Also, certain spots are more windy than others (thus providing the opportunity to generate more power). Can you find the arrangement of turbines contained within the land’s boundaries that produces the most power?