Tax Collector Game

photo by Kelly Sikkema

Source of this activity:By Gary Antonick, New York Times

Tax Collector is played like this: Start with a collection of paychecks, from $1 to $12. You can choose any paycheck to keep. Once you choose, the tax collector gets all paychecks remaining that are factors of the number you chose. The tax collector must receive payment after every move. If you have no moves that give the tax collector a paycheck, then the game is over and the tax collector gets all the remaining paychecks. 

The goal is to beat the tax collector.

Example:
Turn 1: Take $8. The tax collector gets $1, $2 and $4.
Turn 2: Take $12. The tax collector gets $3 and $6 (the other factors have already been taken).

Turn 3: Take $10. The tax collector gets $5.

You have no more legal moves, so the game is over, and the tax collector gets $7, $9 and $11, the remaining paychecks. 

Total Scores:
You: $8 + $12 + $10 = $30.
Tax Collector: $1 + $2 + $3 + $4 + $5 + $6 + $7 + $9 + $11 = $48. 

Questions:

Is it possible to beat the tax collector in this $12 game? If so, how? What is the maximum score you can get?

Bonus: What if you played the game with paychecks from $1 to $24? How about $1 to $48?

 

Lockers and Bulbs

Task 1 (Source: Illustrative Math)

The 20 students in Mr. Wolf's 4th grade class are playing a game in a hallway that is lined with 20 lockers in a row.

• The first student starts with the first locker and goes down the hallway and opens all the lockers.
• The second student starts with the second locker and goes down the hallway and shuts every other locker.
• The third student stops at every third locker and opens the locker if it is closed or closes the locker if it is open.
• The fourth student stops at every fourth locker and opens the locker if it is closed or closes the locker if it is open.

This process continues until all 20 students in the class have passed through the hallway.

1. Which lockers are still open at the end of the game? Explain your reasoning.
2. Which lockers were touched by only two students? Explain your reasoning.
3. Which lockers were touched by only three students? Explain your reasoning.
4. Which lockers were touched the most? 

Make 10 Puzzles

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

Source: @Make_to10

 

Math Taboo Game

 

 

[download the cards from here]