GRADE  7-8 / Age 12-14

The Five Challenges

1.  Would you rather have your height in stacked nickels or in quarters laid end-to-end? Why? (Note:  For purposes of this problem, we will say that these are round coins with the following measurements:  

Quarter:  Diameter - 15/16 in.  Thickness - 1/16 in.

Nickel:   Diameter - 13/16 in.    Thickness - 1/16 in.


2.  At a concert are four seats in a row.  Philip must sit next to Felice but not next to Tamika.  If Tamika will not sit next to Jon, who is sitting next to Jon?  

3.  A football team boasts that all the numbers on  their jerseys are prime numbers under 100.  What is the largest number of players the team could have?

4.  In how many different ways can you divide a square into 4 congruent shapes?

5.  A bug crawls around the outside of a rectangle that measures 6.5 cm by 8.5 cm.  If the bug stays 3.5 cm from the rectangle at all times, what is the area, to the nearest cm squared, of the region bound by the path of the bug?

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