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Fakery, Fudge & Fibonacci

Main Line Math Circle

November 19, 2025

Bill Hawkins

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Schedule

  • 5:00 - 5:10 Missing $ Puzzle/Greetings
  • 5:10 - 5:40 Fibonacci Problems
  • 5:40 - 6:10 Pizza
  • 6:10 - 6:40 Missing Square Puzzle
  • 6:40 - 7:00 Connections between Fib & Missing Square Puzzle

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Welcome!

  • As you enter be sure to check in!
  • Sit down anywhere you’d like - but please don’t move the chairs to form large groups.
  • Introduce yourself to group mates as they arrive.
  • We’ll get started soon - in the meantime give the puzzle a try!

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Puzzle

Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.

On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. So, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself!

As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1?

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Thanks!!!

  • Support for the Main Line Math Circle is provided by the Mathematical Association of America and the Mary P. Dolciani Halloran Foundation.
  • Thanks to the Villanova Department of Mathematics and Statistics for the space.
  • Thank you to our volunteer teachers: Mr. Hawkins (director), Mrs. Hawkins, Mr. Vaccaro
  • Thank you to our high school mentors!
  • Thanks to our Villanova volunteers: Dr. Haymaker (director), Dr. Volpert, VU students
  • Thank you all for coming out.

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Joke Time!

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What is a Mathematicians favorite snack?

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Fibonacchos!

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Why was 4 afraid of 5?

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Because…

1,1,2,3,5,8,13,21,34,55,89

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Would you like to hear another Fibonacci joke?

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Intermission

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Dessert

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ALL YOU CAN EAT

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Now you see it, now you don’t…

With your group, create two possible arrangements for the puzzle pieces. In one, fit everything into a triangle. In the other, leave one square missing. How is this possible????

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Now you see it, now you don’t…

What are the areas of the individual puzzle pieces?

What is the total area of the puzzle?

Can you explain how this is possible?

Challenge: What does this have to do with Fibonacci?????????????

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Let’s Make Some Connections!

Where do Fibonacci Numbers Appear in this Missing Square Puzzle?

Why do Fibonacci Numbers Appear in this Missing Square Puzzle?

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Let’s Make Some Connections!

What do you notice?

What do you wonder?

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Another Puzzle?

Do you notice Fibonacci Numbers in this one?

Why do Fibonacci Numbers Appear now?

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Let’s Make Some Connections!

What do you notice?

What do you wonder?

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Summary

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  • Further reading:
    • Online encyclopedia of integer sequences: https://oeis.org/A000045
    • For more math circle: Join us on December 17 (same time)