Determine the sum of all integers between 1 and 2019 that don't contain the digit 7

Question

the number 254 does not contain the digit 7. The number 107 does contain the digit 7. Determine the sum of all integers between 1 and 2019, inclusive, that don't contain the digit 7.

Answer 1

I got 1,446,620

Here's how I got it, using EXCEL...

Considering only the numbers 1-100:

1 2 3 4 5 6 8 9 10

11 12 13 14 15 16 18 19 20

21 22 23 24 25 26 28 29 30

....

61 62 63 64 65 66 68 69 80

81 82 83 84 85 86 88 89 90

91 92 93 94 95 96 98 99 100

There are 81 numbers ... the total of which is 3862

The 100s will behave the same way. Since there are 81 of these, each one being 100 larger

than the first group, the total then shall increase by 81 x 100 + 3862 = 11962

THe 200s will behave the same way. SInce there are 81 of these, each one begin 200 larger

than the first grouop the total then shall increase by 81 x 200 + 3862 = 20062

the pattern continues until you hit the 600s... you may NOT include 700 but must include 800

So this particular subtotal is 600*81 + 800-700 = 52562

The following table gives the subtotals

1-100 3862

100s 11962

200s 20062

300s 28162

400s 36262

500s 44362

600s 52562

800s 68662

900s 76762

1000s 84862

1100s 92962

1200s 101062

1300s 109162

1400s 117262

1500s 125362

1600s 129700

1800s 149662

1900s 157762

FInally , we add 2000 - 2006, 2008-2016, 2018-2019