### Brain Teasers

# Physical Math

Due to cutbacks at the local high school, physical education and mathematics were combined into one class. This made for some interesting "exercises". One of the questions on this term's final exam stated:

From a starting position walk to the right a distance (in feet) represented by the first prime number. Then turn right 90 degrees and walk a distance represented by the 2nd prime number, and so on, until all prime numbers less than 100 have been accounted for. Then answer the following questions.

a) How far have you walked?

b) How far (to the nearest inch) do you have to walk to return to your starting position?

From a starting position walk to the right a distance (in feet) represented by the first prime number. Then turn right 90 degrees and walk a distance represented by the 2nd prime number, and so on, until all prime numbers less than 100 have been accounted for. Then answer the following questions.

a) How far have you walked?

b) How far (to the nearest inch) do you have to walk to return to your starting position?

### Hint

Do it on paper, unless you need the exercise!### Answer

a) You have walked 1060 feet.b) You have to walk 73 feet, 9 inches

Explanation

There are 25 prime numbers between 1 and 100, neither of which is prime. (No, 1 is not prime.) So you will walk in an expanding square with sides of length 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 feet. This is a total of 1060 feet.

The net result of your turns will be that you are 56 feet ahead of your starting position.

(2+11+23+41+59+73+97)

- (5+17+31+47+67+83)

You will also be 48 feet to the left of your starting position.

(7+19+37+53+71+89)

- (3+13+29+43+61+79)

To calculate the distance back to the starting position, calculate the length of the hypotenuse of the right angle triangle with legs that are 56 and 48 feet long. This is 73.756 feet, or 73 feet, 9 inches.

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