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A street has 50 houses on each side, for a total of 100 houses. The addresses on the south side of the street form an arithmetic sequence, as do the addresses on the north side of the street. On the south side, the addresses are 1, 5, 9, etc., and on the north side they are 3, 7, 11, etc. A sign painter paints house numbers on a house for 1$ per digit. If he paints the appropriate house number once on each of these 100 houses, how much does he earn?

 Sep 24, 2020
 #1
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The sign painter earns a total of $424.

 Sep 24, 2020
 #2
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The numbers on the houses on the South side of the street are: 

(1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197) = 122 digits.

 

The numbers on the houses on the North side of the street are:
(3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191, 195, 199) = 123 digits


122 + 123 = 245 - Total number of digits on all 100 houses.

245 digits x 1 dollar per digit = 245 - dollars - what he/she will earn on painting the numbers on the 100 houses.

 Sep 24, 2020

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