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The owner of a local jewelry store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave \(\frac{1}{2}\) of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?

The owner of a local jewelry store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave \(\frac{1}{2}\) of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally? Correct Answer 36

Explanation:

Since thief escaped with 1 diamond.

Before 3rd watchman he had (1 + 2) × 2 = 6

Before 2nd watchman he had (6 + 2) × 2 = 16

Before 1st watchman he had (16 + 2) × 2 = 36

Alternative method:

Check with choices.

Related Questions

The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave $$\frac{1}{2}$$ of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?
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