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Three Classical Problems For All (Ages...or Time)


In 1982, Rosalie Jensen and David O'Neil (professors at Georgia State University) published a collection of "Classical Problems for All Ages." Try your hand at these....some you may recognize as well.

[CP#1] Kermit the frog fell in a hole that was 10 meters deep while he was taking a walk in the woods. Each day he could only jump 3 meters up the side of the hole. Each night he slid down 2 meters. How many days did it take Kermit to get out of the hole?

[CP#2] Ms. Green, the art teacher, needs 2 liters of water to make a clay mixture for her students. She has two unmarked pails, a 3-liter pail and a 4-liter pail. Using only these pails, how can she get 2 liters of water?

[CP#3] After a forest fire in a national park, the park rangers must relocate eight animals whose homes were destroyed. Each van used for this job can carry no more than 100 kilograms. The weights of the animals in kilograms are 45, 38, 32, 26, 21, 16, 9, and 2. Help the forest rangers by finding at least one way to put all the animals in the two vans available.

Jensen and O'Neil claimed they picked these problems because:

  1. They "focus on strategies of solution rather than on performance of complex arithmetic operations."
  2. They can be adapted and extended to different age levels and abilities.
What three classical problems would you pick...and why?

 

Source: Arithmetic Teacher, January 1982, pp. 8-12.


Hint: Draw pictures, make tables, make and test conjectures, look for hidden relationships...and all that good stuff known as "classical" heuristic approaches....

 


Solution Commentary: These problems are "classics"...and will not be spoiled by my providing answers. Play with the problems...share your solutions...come to agreement.