SNAP Mathfairs
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    • Organizing & Preparing for the Fair
    • Choosing a Theme
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    • Some Typical Projects
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  • Grading
    • Assessment Checklist (Grade 7)
    • Evaluation Guidelines (Grade 9)
    • Rubric for a Math Fair (Grade 12)
    • Marking Guide (Grades 5 and 6)
    • Math Fair Club Evaluation (Grades 4 and 5)
  • Resources & Contacts
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  • Puzzles
    • Level 1 Puzzles >
      • Spoke Sum
      • Number Wheel
      • Buggy Jump
      • Pyramid
      • Nine Men in a Trench
      • Star Jump
      • Circle Jump
      • Circle Jump II
      • Four Cottages
      • Free the Animals
      • Sam's House
      • About the Solutions
      • Solutions - Level 1
    • Level 2 Puzzles >
      • Neighbourhood Sums
      • Eight Squares
      • Soko Puzzle I
      • Soko Puzzle II
      • Abdication
      • Regime Change
      • Stairways to Heaven
      • Catacombs
      • About the Solutions
    • River Crossing Puzzles >
      • The fox, the goose, and the grain
      • The fox, the goose, and the grain, and the dog
      • The mouse, the elephant, the dog, and the cat
      • Soldiers and children
      • Animal Crossing
      • The Three Thieves
      • The Missionaries and the Cannibals
      • Quarrelsome Boys
      • Jealous husbands
      • A Handful for the Farmer
      • The farmer, his children, and their pets
      • About the Solutions
    • Sudoku-Type Puzzles >
      • Cats, Cows, and Pigs
      • Latin Squares
      • Apple and Bananas I
      • Apple and Bananas II
      • Apple, Bananas, and Cherries
      • Four Skyscraper Puzzles
      • Colourful Cats and Pigs I
      • Colourful Cats and Pigs II
      • The Wizard's Hats
      • Four Colours
      • About the Solutions
    • Other Puzzles >
      • Catch the Thief
      • Cherry Glasses
      • Coin Jumping I
      • Coin Jumping II
      • Evensies
      • The 22 Game
      • Switch Positions
      • Spellbound Frogs
      • The Die Hard Jugs
      • About the Solutions
    • About the Solutions
  • About SNAP
    • Our Mandate
    • Our Supporters
    • Who Are We?
    • Curriculum Connections
    • The SNAP Approach and "Inquiry-Based Learning"
    • Some History
  • Gallery

Four Cottages

Below is a map of a circular road. The distance between the dots is 1 kilometre. There are two houses on the road, and two more house are going to built. The local council has asked you where they should be put so that given any of the distances from 1 to 12, there are two houses that are that far apart. Of course, the two houses that are there are separated by 1 kilometre or 12 kilometres, depending upon what direction you travel, so you only have to concern yourself with the distances of 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
Picture
This puzzle is inspired by The six cottages from Dudeney's 536 puzzles and curious problems.