The mystery of the tower

Introduction

After the children have understood binary code with the game of the TETRADICE this game can be presented as a challenge. It should be played singly or in small groups, but every child must manage to solve it.

Preparation

We are going to use a tower of values with base in the binary code. On the base we place the highest value in binary code. The base will be red, which is worth 8 points, the next level blue, which is 4 points, then green (2 points) and finally yellow (one point).

We have on the table or on the ground three spaces and we place the tower on one of these spaces.

Procedure

  1. The facilitator says: Lets play you are a tower builder. I place here a tower made of pieces each of which is worth some points. What you have to do is to move the tower to another space. But we have two rules:
    1. First, since there is only one derrick only the upper piece can be moved at a time, and
    2. Second, you cannot put a piece above another one that is worth fewer points.
  2. To facilitate the understanding of the rules we can ask the children questions such as: Can you move the green piece that is under the other? Well then move the yellow one… Can you place the green piece above the yellow one? When the child places the piece onto another space then she will have understood the rules of the game.
  3. Now we must reinforce the process by saying that we should try to use the fewest possible movements in order that the derrick does not waste too much gas.

    This dilemma can be solved in 15 movements and when the answer is reasoned it needs more time. The number of movements is exactly equal to the value of the tower.

    It is important to remind the child not to think it, so that she follows her intuition. The facilitator must not interfere.

    The challenge is raised. The child might take minutes, hours, days, months or years to solve it; the important thing is that the child faces the challenge.

  4. After the challenged is solved ask the child: which it is the minimal number of movements?
  5. Ask the child to add up the points values of each piece; 8 the red one + 4 the blue one + 2 the green one + 1 the yellow one equals 15.
  6. Ask: could it be that the minimal number of movements is related to the point value of the pieces? How could we verify it?
  7. Remove the red piece and request the child to do the challenge again.
  8. The child will do the checking. Blue +green + yellow add up to 7 and 7 movements are needed.
  9. Challenge the child to check if this is by chance and how to verify it.
  10. Leaves only the green and yellow pieces (adding 3 points) and ask the child how many movements will she need.
  11. Then request the child to verify it.
  12. When the child does it, she will have solved the mystery of the tower.