CHALLENGE

How much was that again?

An absent-minded bank teller switched the dollars and cents when he cashed a check for Jana, giving her dollars instead of cents and cents instead of dollars.  After buying a five-cent stamp, Jana discovered that she had exactly twice as much left as the amount of her original check.  What was the amount of the check?

Which way did they go?

Moses was hiking from Harper to Belmont along the Winding Trail, which also passed through the town of Springfield. Forty minutes after he left Harper, Moses saw a sign reading, "From Harper to here is half as far as it is from here to Springfield."  Moses hiked another 11 miles and saw a second sign reading, "From here to Belmont is half as far as it is from here to Springfield."  Moses hiked 1 more hour and reached Belmont.  If he hiked at the same pace all the way, what is the length of the Winding Trail between Harper and Belmont?

Don't fence me in...

Rebekah is planning her garden for the spring.  She has ten square garden plots, each of the same size.  One will be for carrots, one for lettuce and so on.  She wants to arrange the plots so each of them has at least one side in common with another garden plot.  When she finishes arranging the plots, she plans to put a rabbitproof fence around the entire plot.

A)  How would Rebekah arrange her garden plots so that she would use the least amount of fencing?  How would she arrange her plots to use the largest amount of fencing?

B)  In general, what happens to the smallest (largest) amount of fence as the number of garden plots increases? Justify your answer.

Be sure to use your MathWorld Interactive six problem-solving steps. Have fun!