Magic numbers

Magic numbers are number that contains 6 or 8, but not both.

So, the following are magic numbers: 6, 8, 666, 888, 106, 1623, 1457864

And the following aren't magic numbers: 68, 1086, 6008, 346893, 0348644

Now, find the count of magic number within a range. So the count within the range 1 - 10 is 2 and the count for the range 1 - 100 is 34.

Question: What is the count of magic numbers for the range 1 - 1,000,000,000?

PS: I was asked this question for an interview. I was given 8 test cases the first 6 could easily be solved computationally, but the last two were for the ranges $1 - 1,000,000,000$ and $1 - 2^{52}$ are unlikely to be solve computationally.

#NumberTheory

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Comments

I estimate 100 - 10,000 magic numbers.

A Former Brilliant Member - 1 year, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$