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How many of the natural numbers from 1 to 800, inclusive, contain the digit 6 at least once?

 Oct 13, 2021
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Hello,

 

from one to a hundred, 10 numbers have the number 6 as the ones digit, whereas a zero is enough for 66.

 

Now the tens digit could also be a 6, i.e. a total of 10, which means that there are 19 numbers,

 

from one to one hundred, that have at least one 6 (6,16,26,36,46,56,60,61,62,63,64,65,66,67,68,69,76,86,96).


From 100 to 200, only 10 numbers can have a 6 in the ones place and 10 in the tens place and the hundreds place 0,

 

because it only starts with a one. Finally, there are 19 numbers that have at least one 6

 

(106,116,126,136,146,156,160,161,162,163,164,165,166,167,168,169,176,186,196).

 

From 200 to 300 there are also only 19 numbers, from 300 to 400 also only 19 numbers,

 

from 400 to 500 also only 19 numbers, from 500 to 600 also only 19 numbers,

 

but from 600 to 700 all numbers that total 100 have a 6,

 

then from 700 to 800 also only 19 numbers. Finally, this gives (\(19+19+19+19+19+19+100+19=233 \)) numbers.

 

Straight

 Oct 16, 2021

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