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Can all numbers be written as fractions? Don't be irrational - understand some of the fundamental classifications of numbers.

Find the smallest positive integer whose square consists of 5 identical leading digits.

As an explicit example, \( 149^2 = 22201 \) would be the answer for 3 identical leading digits.

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You have to place dots along a strip such that:

- The first two dots are in the different halves of the strip
- The first three dots are in the different thirds of the strip
- The first four dots are in the different fourths of the strip, and so on.

What is the maximum number of dots you can place on the strip?

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Let \(\displaystyle \frac ab\) be the smallest of the fractions that are greater than \(\displaystyle \frac {13}{15}\) where \( a,b < 500\) are positive integers.

What is the value of \( a+b\)?

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