There once was a boy who spent all his time dreaming about getting rich. " I would do anything to be rich". The devil, hearing this, appeared before the boy and offered to make him rich. "See that bridge?" said the devil. Just walk across and I will double your money you have now. In fact, each time you cross I will double your money. There is just one thing you must give me \$24 after each crossing. The boy agreed. He crossed the bridge, stopped to count his money and, and sure enough, it had doubled. He paid the devil \$24 and crossed again. Again his money doubled. He paid another \$24 and crossed a third time. Again his money had doubled, but this time there was only \$24 left which he had to pay the devil so he was left with nothing. The devil laughed and vanished.

2. Suppose the problem remains the same except that the boy gives up \$30 rather than \$24. Now how much did the boy start with?
3. Suppose the problem remains the same except that the boy crosses four times rather than three times. (He still gives up \$24 each time.) Now how much did the boy start with?

DJ
age 12

Hi DJ,

This is a problem that you need to approach by "working backwards". I am going to do it by drawing a table with 3 rows, one for each time he crossed the bridge. My table has 5 columns:

• The crossing number (1, 2 or 3)

• Amont of money he had before he crossed

• Amont of money he had after he crossed

• Amont of money he paid to the devil

• Amont of money he had remaining
What I know from the start is that the remaining column after the third trip is \$0, and the devil column is \$24 each time.

crossingbeforeafterdevilremaining
1   \$24
2  \$24
3  \$24\$0

Now work backwards.

On the third crossing, after he paid the devil \$24 he had \$0 so he must have had \$24 after he crossed the bridge. Since crossing the bridge doubles his money he must have had \$12 before he crossed the bridge. Thus the remaining money he had after the second crossing was \$12.

crossingbeforeafterdevilremaining
1   \$24
2  \$24\$12
3\$12\$24\$24\$0

Now on crossing 2 he paid the devil \$24 and had \$12 remaining so he must have had \$36 after crossing the bridge. Thus he had \$18 before crossing the bridge.

crossingbeforeafterdevilremaining
1   \$24\$18
2\$18\$36\$24\$12
3\$12\$24\$24\$0

Repeat for the first crossing to find how much money he had to start.

For the second problem, put \$30 in the devil column and repeat the steps. For the third problem add a fourth row to the table.

Cheers
Penny
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