Odd numbers

Number Theory Level 3

What is the greatest number of 3 digits consecutive integers such that they have at least an odd digit?


The answer is 111.

Drop TheProblem by Drop TheProblem , 24, Italy

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2 solutions

Devasish Basu
Aug 9, 2015

Taking the hundredths place to be an odd number gives 100 such numbers. e.g. 500 to 599. Then consider from 489 to 499. These 11 numbers are in continuation with 500 to 599. This gives a total of 100 + 11 = 111 numbers

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Drop TheProblem
Aug 6, 2015

For example from 289 289 to 399 399 ⇒ 399 − 289 + 1 = 111 \Rightarrow 399-289+1=111

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But 89 is not a 3-digit number :P

The idea is clear though.

Also, I don't think you need to say "integer numbers" - "integers" would suffice.

Richard Zhou - 5 years, 10 months ago

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Easily fixed of course: from 289 289 to 399 399 .

mathh mathh - 5 years, 10 months ago

Thanks for the advices. I've also edited my solution, of course 89 is not a 3 digit number xD. The solution is the same as @mathh mathh

Drop TheProblem - 5 years, 10 months ago

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