Challenge Questions

 

Challenge Questions #3 and #4 run from September 1st, 2008 to September 13th, 2008.  Answers may be submitted electronically or traditionally, but must include full solutions/explanations.  Good luck!

 

Challege Question #3:  A farmer has four straight pieces of fencing: 1, 2, 3, and 4 yards in length.  What is the maximum area he can enclose by connecting the pieces?  Assume the land is flat.

 

Challege Question #4:  Using only the numbers 1, 3, 4, and 6, together with the operations +, −, ×, and ÷, and unlimited use of brackets, make the number 24.  Each number must be used precisely once.  Each operation may be used zero or more times.  Decimal points are not allowed. 

 

 Previous Challenge Questions

 

Challlenge Question #1: Jo, Pat, and Kris went on a picnic.  Jo brought two sandwiches and Pat brought three sandwiches, but Kris forgot to bring food.  If the three campers shared their food equally and Kris paid Pat and Jo a total of five dollars for the sandwiches that they shared, how much money should Pat and Jo each get? 

Answer:  Pat: $4; Jo: $1

 

 

Challenge Question #2: A triangle has sides of integral length.  If it is known that two sides of the triangle measure 700 and 800, how many possible triangles can be formed?  (Note: integral length means that the length must be an integer, such as ... -2, -1, 0, 1, 2, ...)

Answer: 1399. 

 

Enjoy the puzzles below!