To solve this problem, we can visualize how the flyers are handed out each day and calculate the total number of people who receive the flyers cumulatively.
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Day 1: David hands out the flyers to 7 people.
- Total people having flyers at the end of day 1: \( 7 \)
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Day 2: Each of the 7 people hands out the flyers to 7 new people.
- Number of new people receiving flyers = \( 7 \times 7 = 49 \)
- Total people having flyers by the end of day 2: \( 7 + 49 = 56 \)
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Day 3: Each of the 49 new recipients hands out the flyers to 7 more people.
- Number of new people receiving flyers = \( 49 \times 7 = 343 \)
- Total people having flyers by the end of day 3: \( 56 + 343 = 399 \)
Therefore, the total number of people who have received flyers by the end of day 3 is \( \boxed{399} \).