A Confusing Story

Some friends bought a sailboat together and shared the cost equally.  If two fewer friends had been involved, each of the others would have pair $3000 more.  If one more friend had been involved, each of them would have paid $1000 less.

How many people owned a share of the sailboat? And how much did it cost?

Which ONE of these is the TRUE statement?

 1) Exactly one of these twelve statements is false.

2) Exactly two of these twelve statements are false.

3) Exactly three of these twelve statements are false.

4) Exactly four of these twelve statements are false.

5) Exactly five of these twelve statements are false.

6) Exactly six of these twelve statements are false.

7) Exactly seven of these twelve statements are false.

8) Exactly eight of these twelve statements are false.

9) Exactly nine of these twelve statements are false.

10) Exactly ten of these twelve statements are false.

11) Exactly eleven of these twelve statements are false.

12) Exactly twelve of these twelve statements are false.

The Racing Terror

A race car driver doubles his average speed every mile in a 3-mile race.  During the first mile, his average speed is 60 miles per hour.

What is his average speed for the 3 miles?

CUBES IN SPACE

Imagine that a 10x10x10 cube made up of 1,000 unit cubes was floating in space.  What is the greatest number of unit cubes that could been seen by an observer at any moment in time?

CLIP TRIANGLES

Suppose you have a chain of 24 paper clips.  Follow the rules below to make triangles:

• Use the whole chain.
• Do not break up the chain
• Make isosceles triangles (two congruent sides & two congruent angles)
• or Make right triangles (remember Pythagoras?)
• but NO EQUILATERAL triangles (all three sides & angles congruent) are allowed !

How many triangles can you make (& what are their sides?)

Which of these triangles has the greatest area?