Puzzler Olympiad

On October 12, more than 100 contestants from some 25 countries will meet in Opatija, Croatia, for the 13th annual World Puzzle Championship. The language-neutral puzzles that follow are typical of the challenges posed at the tournament. The puzzles are adapted from the World Puzzle Championships Omnibus, Volume 1, edited by Will Shortz and Nick Baxter (Random House, 2004), and Mensa Math & Logic Puzzles, by Dave Tuller and Michael Rios (Sterling Publishing, 2000).

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STAKEOUT

1. [Easy] The diagram above represents a city street map. One police officer is positioned at the red dot. Add one more officer so that every point on every street can be seen by at least one of the two patrolmen. Officers can see only down the streets; tall buildings prevent them from seeing across the blocks.

2. [Challenging] Position three police officers at separate locations on the map so every point on every street can be seen by at least one officer. To solve the problem, two of the officers must be able to see each other.

3. [Difficult] Position four police officers on the map so that every point on every street can be seen by at least one officer. Hint: Three of the officers are on the same street (puzzle courtesy of Feniks magazine).

GRIDLOCK

Fill the empty squares in the grids below with either a black or a white circle. In each completed grid, all squares containing white circles must be connected to one another either horizontally or vertically. The same rule applies to all squares containing black circles. In other words, the white circles and the black circles must each form a path through the grid. Small offshoot paths are fine, but they must be connected to the main path by at least one vertical or horizontal adjacency. For example, in diagram 1 the light blue squares must contain black circles. There is no other way to connect the black circle in the bottom right corner to the rest of the black circles using only horizontal or vertical adjacencies. One more rule: No two-by-two region can contain four circles of the same color. So, the pink square in diagram 1 must contain a black circle.

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HUBBUB

In each of these diagrams, draw spokes to connect neighboring hubs. To get you started, we’ve filled in a few spokes in diagram 1. The spokes can run horizontally, vertically, or  diagonally, but they may not cross one another. The number in each hub indicates how many spokes connect to that hub, and all hubs are interconnected. Note: There may be more than one answer for each grid.

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