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How many 5's would you write if you were to write all the numbers from 1 to 1,000,000?
Question
#62189. Asked by melnnat.
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carlos1942
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from 1 to 100 there are 20 fives. So from 1 to a millon, there are 200.000
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gmackematix
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Imagine we add zeros to the start of the lower numbers so that each is a six figure number.
Counting from 000000 to 999999 will take 6,000,000 digits to write down and each digit will occur an equal number of times.
That means that 600,000 fives would be written.
Ignoring the initial zeros and counting from 1 to 1,000,000 makes no difference to the number of fives written so the answer is 600,000.
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minuscule_
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I get it gmackematix, there's a pattern. One 5 in the first 10 numbers, Twenty 5's in the first 100 numbers, or 1.10^0 in 10^1, 2.10^1 in 10^2, 3.10^2 in 10^3, ..., 6.10^5 in the first 10^6 numbers, etc. You can be my teacher anytime.
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