SNAP Mathfairs
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  • Organizing
    • Organizing & Preparing for the Fair
    • Choosing a Theme
    • Different Types of Displays
    • Some Typical Projects
    • Who to Invite
    • Optional Timelines
    • Math Fair Club
  • 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
    • Puzzle Sources
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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

Stairways to Heaven

An archaeologist found a Mayan temple shaped like a hexagonal pyramid with four levels. Each of the six sides had four staircases leading from level to level all the way to the top. The number of steps in the staircases varies, so the archaeologist sent four assistants to count them. The first assistant counted the steps in each of the six staircases leading to the level one, the second counted the steps in the six staircases leading from level one to level two, and so on, and they produced the following report:

Ground to Level I:53,50,37,39,42,51.Level I to Level II:37,21,30,25,25,35.Level II to Level III:29,23,17,19,11,17.Level III to Level IV:11,5,7,3,4,9.The archaeologist recorded the numbers on four hexagonal pieces of paper and pinned them at the center to form the model shown below. He realized that although all the assistants visited the staircases in clockwise order, they did not all start from the same side. The total number of steps altogether is 600, so the archaeologist thought that there must be 100 steps on each side.

Rotate the levels so that as many of the six sides as possible have exactly 100 steps.

Picture
An old puzzle revived by RGee Watkins, Hemet, California.