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 From B. Lee Clay

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Multiplying a repeating 7's number by 99

1. Choose a repeating 7's number (777, etc.)
2. Multiply it by 99
3. The product is:
- the first two digits are 76
- the next digits are repeating 9's (two fewer than repeating 7's in the original number)
- the final two digits are 23

Example:

1. If the first number is 7777:
2. First two digits are 76.
3. Next digits are repeating 9's -- two fewer than repeating 7's in the original number: 99.
4. Last two digits are 23: 23.
5. So 99 × 7777 = 769923.

See the pattern?

1. Next pick is 777777:
2. First two digits are 76.
3. Next digits are repeating 9's -- two fewer than repeating 7's in the original number: 9999.
4. Last two digits are 23: 23.
5. So 99 × 777777 = 76999923.

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13 January 2009
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