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Challenge 299 : Fishy Business

A description of the book “The Taxonomy and Characteristics of Red Herrings: 4th Edition” by Fay Kimberly Fish reads as follows:

“An inspiring encyclopaedia on the classification and (as of 2nd edition) behaviour of Red Herring native to British waters. Released in 1960 and revolutionising the field of freshwater Red Herring study, the incredible Fay K Fish was, in only 20 pages, able to change everything previously known about these illusory creatures: their average width turned out to be only 0.512 metres, their lifespan twice the previous number once you convert it to inches, and estimates for how many pages this information could be communicated in were discovered to be much more difficult than previously anticipated. Of course, the book has only grown in the past years, needing 1890 digits in total to print, and under special circumstances insisted upon by the author, every 10th digit must be printed in bold. The current edition can be measured with only 2 average specimens, when put lengthwise from tip to tail; an achievement barely thought possible only 41 years ago. Truly Madam Fish is a champion amongst fish.”

The question is, can you filter through all the useless information here and figure out how many pages this 4th volume will have?

And secondly, how many pages pass before a bold digit appears?

Hint: The frequency of bold digits per page will change as we reach different ranges of numbers, it's good to write out the list of numbers and mark every 10th digit (starting from the left).

Submit your solution

Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.

 

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