Samples

1.       Harry, Ron, Hermione, Ginny, and 7 others are representing Gryffindors to compete for the House Cup. Each team has a team captain plus 10 team members. For their 1st challenge, they need to figure out the following: 

 

Ten team members will be blindfolded and any integer between 1 and 10 (inclusive) will be written on their forehead.  Numbers can be repeated.   The blindfolds then were removed so a team member can see the number on other team members but not his/her own number.  The team captain, who can see all 10 numbers, has a crystal ball which can be given to one of the 10 team members.  Nobody is allowed to talk to each other and the ball cannot be passed on to another team member. With that, if all of team members can figure out the number on his/her own forehead, then the team will pass the challenge.

Can you help them to discuss a strategy beforehand so that the team can work together to solve the challenge?

I Wonder… What if there are 16 numbers, instead of 10? What could the team captain do to provide information to his team members silently?


2.       Which one doesn’t belong?                                         

I Wonder… Could there be multiple answers? Could other similar problem have multiple answers too?

3.   Last Minion Standing: Kevin was playing the Last Minion Standing game with other minions.  The rule of the game is simple: 

a.      There is a big round table with seats surrounding it.

b.      There are as many seats as the minions playing the game

c.       Each seat has a number (from 1 to n) and it is incremented going clockwise (except of course the last number n is next 1)

d.      Every minion selects a seat but stand behind it to start the game.

e.      The minion behind seat #1 get to go first in the game.

f.        The minion has the turn makes the next minion who is still standing in the game in the clockwise direction to sit down.

g.      The turn goes to the next minion who is still standing in the clockwise position.

h.      The last minion who is still standing wins the game

What seat number should Kevin choose if there are a total of 43 minions to win?

I Wonder…what happen if the rule is changed so instead of making the next minion sit down, we skip one minion and make the one after the next minion sit down.  Where should Kevin be sitting.

4.   In the land of Knights and Knaves, knights always tell truth and knaves always tell lies.

  1. Alice mumbled something incomprehensible.  Bob said "Alice said that she is a knave."  Code said "That's a lie; don't believe Bob."   So who are Bob and Cody>?  Knight or Knave?
  2. There are only two people, Adam and Beth.  Adam said "At least one of us is a knave."  Who are Adam and Beth?
  3. Alice again said something incomprehensible.  Brad said that Alice said that there is one knight among us."  Cindy said, "That's a lie, don't believe Brad."  Who are Brad and Cindy?

I Wonder… Can I make my own problems with Knights and Knaves?

5.   Chocolate Breakup. Two players take turns breaking a piece of chocolate consisting of 5 x 10 small squares. At each turn, a player breaks the chocolate along the division lines of the squares and pass one of the two pieces to the opponent. The player who first obtains a single square of chocolate wins. (And the winner gets all the pieces of chocolate.)

6.  Can you cut a piece of paper to look like in the picture below?  no glue or tape



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