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| Math Central | Quandaries & Queries |
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Question from bevaz, a student: A ruler orders his chamberlain to collect an army from 30 houses. The servant goes to the first house alone and collects one man. At each house after that he takes the same number of men as he has already collected, so at the second house he goes with one other and so on. How many men did he collect in all? |
Bevaz,
I reworded your question as I wasn't sure if the chamberlain was to be considered as part of the army or not. I worded it so he is not. If I am incorrect you can modify my strategy to cover that situation.
I decided to use a table to keep track of what happens at the first few houses.
| House number | Number collected at this house | Number collected in total |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 2 | 4 |
| 4 | 4 | 8 |
At the first house he collects one man. He goes to the second house with this man so at the second house he collects one man to match the one he has already, so now he has 2 men.
He goes to the third house with these 2 men and collects 2 more to match them and now he has 2 + 2 = 4 men. He goes to the fourth house with 4 men, collects 4 more and now has 8 men.
Add a couple of more rows to the table. Do you see a pattern in the final column? What will be the number in the final column of row 30 of the table?
Penny
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