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# Question and Solution

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The Question:

If you had the following choice of salary methods, which would you choose and can you explain why this is your choice?

Option A: One billion dollars per year plus health coverage, a yearly expense account of \$1 million, and a \$100,000 car.

Option B: The amount of money obtained by putting \$1 on one square of a chessboard, \$2 on the next, \$4 on the next, \$8 on the next, and so on until all 64 squares are filled.

The Solution:

Students, working in small groups, typically attack this problem in the following way.

Step 1. Draw a chessboard and begin putting numbers in each square.

Step 2. As the numbers begin getting larger, students usually switch to a chart system like the following.

Square Total Money So Far

1 \$1
2 \$1 + \$2 = \$3
3 \$1 + \$2 + \$4 = \$7
4 \$1 + \$2 + \$4 + \$8 = \$15
etc. etc.

Step 3. Once they see a pattern in the chart, they can generalize, that is, generate a formula. In this case, the formula is 2x - 1.

Finally, they can solve the problem by simply plugging in 64, for 64 squares, into the formula as x. The answer is \$18,446,744,070,000,000,000. (This has been rounded off.)

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