The Math Problem Directory archives problems from Math Olympiads from all over the world.

The problems below are fairly classic.  I plan to add solutions separate solutions for each one.

1.   A friend can only drink 2% milk.  You only have 4% milk and 1% milk.  How can you prepare 8 fluid ounces of 2% milk for your friend?

2.  How far apart are the points (1,2) and (5,7)?

3.  Which has a greater area: A triangle with sides 5, 5, and 6   or   a triangle with sides 5, 5, and 8?

4.  I'm thinking of a two digit number.  If you subtract the reversed number, the result is the same as if you added the digits together.  What is the number?

5.  A quadrilateral has sides as follows(going clockwise): 3, 4, 5, and X.  The diagonals of the quadrilateral are perpendicular to each other.  What is X?

6.  An alley is 12 feet wide.  A 13 foot ladder and a 15 foot ladder are put into this alley, so that they cross in an X and both touch each wall.  How high up do the ladders cross?

7.  You're camping, and have rope, plenty of trees, and have an 8 foot by 10 foot tarp.  A rainstorm is coming, and you need to store 90 cubic feet of camping stuff.  Find the formula for the volume under an inverted-V style tent, based on a height of X at the top of the tent.  Is it possible to store everything?

8.  A cannon set up parallel to the ground at a height of 5 feet fires a cannonball at 300MPH.  How far does the cannonball go before it hits the ground?  Assume that the ground is absolutely flat.

9.  You toss a baseball straight up into the air at 90KPH (Kilometers per Hour).  Assume you release the ball at a height of 2.5 meters.  How long until the ball hits the ground?

10.  You have a 8 foot by 10 foot piece of cardboard.  You plan to make a box without a top by cutting a X by X square out of each corner, then folding up what remains.  What is the formula for the volume of this box, based on X?

11.  What is the area of a triangle with Medians measuring 3, 4, and 5?

12.  How many different fair dice have 24 sides?