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problem

Winning team

11 to 14

Nine cross country runners compete in a team competition in which there are three matches. If you were a judge how would you decide who would win?

problem

Triangle ABC has altitudes h1, h2 and h3. The radius of the inscribed circle is r, while the radii of the escribed circles are r1, r2 and r3 respectively. Prove: 1/r = 1/h1 + 1/h2 + 1/h3 = 1/r1 + 1/r2 + 1/r3 .

problem

Cut cube

16 to 18

Find the shape and symmetries of the two pieces of this cut cube.

problem

Eleven

11 to 14

Replace each letter with a digit to make this addition correct.

problem

Team scream

7 to 11

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

problem

LOGO challenge 6 - triangles and stars

11 to 16

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

problem

Magic W wrap up

16 to 18

Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.

problem

Couples

11 to 14

In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?

problem

A circuit problem

16 to 18

Explore the voltages and currents in this interesting circuit configuration.

problem

Circular inscription

14 to 16

In the diagram, the radius of the circle is equal to the length AB. Can you find the size of angle ACB?

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Winning team

Area i'n it

Cut cube

Eleven

Team scream

LOGO challenge 6 - triangles and stars

Magic W wrap up

Couples

A circuit problem

Circular inscription