Amazing love! How can it be

that thou, my God, shouldst die for me?

Flag of Red Cross |

Flag of Switzerland |

*Christmaths*puzzles, which would appeal to above-average elementary and middle-school math students and their teachers.

**1. Squares in a Cross**

A solid Greek cross can be formed by putting together five cubes, or from a number of squares. How many squares are there?

**2. Tessellating and Dissecting Crosses**

(a) Show how Greek crosses can form a tessellation.

(b) How can an infinite number of dissections from a cross tessellation produce a square?

**3. A matchstick Puzzle**

The cross on the left is made up of 19 matches. Move 7 of them to make a pattern consisting of four squares.

**4. The Area of a Cross**

A cross is made up of five congruent squares. If

*XY*= 10 cm, what is the area of the cross?

**5. Cross into Rectangle**

Using only two straight cuts, divide the cross on the right into three pieces and reassemble them to form a rectangle twice as long as it is wide.

**6. Five-piece Square into Cross**

Cut a square into five pieces and rearrange them to form a Greek cross, as shown below.

**7. Four-piece Square into Cross**

Cut a square into four pieces and rearrange them to form a Greek cross, as shown below.

**8. Cross into Hollow Square**

The Greek cross on the left has a square-shaped hole in the center.

(a) Rearrange the pieces to make a square that has a hollow cross inside.

(b) Rearrange the pieces so that the resulting figure is a square that is rather smaller than the previous "hollow" one.

**9. The Cross and the Crescent**

**Reassemble the seven pieces of the crescent to make the Greek cross.**

**10. The Rolling Disc**

In the figure below, each side of the cross is 10 cm long. A small circular disc of radius 1 cm is placed at one corner. If the disc rolls along the sides of the figure and returns to the starting position, find the distance traveled by the center of the disc.

**Selected answers/solutions**

1. 22 squares.

4. 100 cm².

5.

7.

8.

**10. (104 + 2**

*π*) cm

**Reference**

Yan, K. C. (2011).

*CHRISTmaths: A creative problem solving math book*. Singapore: MathPlus Publishing.

© Yan Kow Cheong, March 31, 2013.

Code: WR3ZTVKVUW9Z

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