“It Balances!” Friend, Jan. 1982, 33

Exploring:

# It Balances!

Place a hexagonal pencil on a flat surface so that a twelve-inch ruler can be balanced on it. Ordinarily, the ruler’s midpoint should be directly over the pencil.

Next, place a penny on each end of the ruler without disturbing its balance. Now, leave the penny in place on one end of the ruler and find where *two* pennies can be placed on the opposite end of the ruler to keep it in balance. When this has been done, notice the number of inches they are placed from the pencil and then find the number of inches from the pencil that *three* pennies must be placed for the ruler to balance.

Finally, multiply the number of pennies by the number of inches that each group of pennies was placed from the pencil and compare your answers.

In each case, the answer should be exactly the same unless an error has been made. When one penny is six inches from the pencil, the product is six. When two pennies balance with the other side, its product must also be six, so the pennies should be three inches from the pencil. For the same reason, three pennies must be two inches and six pennies one inch from the pencil.

Can you place three pennies so that they are five inches from the pencil on one side, and then find where five pennies should be placed on the other side?