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A lumberjack chopped wood, each time cutting a piece of wood in half. When he finished he observed that after making 53 cuts he had 72 pieces of wood. With how many pieces did he begin?

Question

A lumberjack chopped wood, each time cutting a piece of wood in half. When he finished he observed that after making 53 cuts he had 72 pieces of wood. With how many pieces did he begin?

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Solution

The lumberjack starts with one piece of wood. Each time he makes a cut, he adds one more piece of wood. So, if he made 53 cuts, he would have 54 pieces of wood (53 from the cuts and the 1 he started with). However, the problem states that he ended up with 72 pieces of wood. This means that he must have started with more than one piece of wood.

To find out how many pieces he started with, subtract the number of pieces he should have had if he started with one piece (54) from the total number of pieces he ended up with (72).

72 - 54 = 18

So, the lumberjack must have started with 18 pieces of wood.

This problem has been solved

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