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How many words are there in the daily edition of The Times? How many songs are stored on iPods in the UK? How many spikes

are there on the back of a hedgehog? These and other provocative questions await you, in preparation for your interview with

Oliver Wyman.

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HEDGEHOGS, IPODS, BIRTHDAYS:Puzzles to ponder ahead of your interview.

NEWSPAPERHow many words are there in the daily edition of The Times?

When faced with a structured estimation question such as this one, it is essential to make your assumptions and thought-process clear at the

beginning.Y ou s hould s ta rt by la y ing out a ny k e y princ iple s whic h will he lp y ou s implify the proble m getting the answer exactly right

isn' t required. In this example, the key principle is to come up with the number of text-only pages in a standard copy, and combine this with an

estimate of words per text-only page. One way of simplifying the problem is to exclude text in adverts and diagrams, to make it easier to covert a

standard page into a fraction of text-only page. Another simplification is to exclude any additional supplements.

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Once you have set out any key principles and simplifying assumptions, break the problem into sub-questions or a logic flow to show the interviewer

how you are thinking. One possible set of sub-questions is shown below:

Question 1: On average, how many pages are there in the daily Times, excluding supplements?

You would be expected to answer this question with a reasonable estimate based on knowledge, for example by breaking down the paper into its

constituent sections (UK news, World news, Business, Sport, Court & Social etc). The interviewer would also help guide you in the right direction if

needed. The answer is approximately 6 5 pa ge s.

Question 2: How much of the paper is taken up by adverts?

The two most common advertisement sizes in the Times are full page and 1/3 page.Estimating the share of advertisements is not trivial but a good

approximation would be that 20% of the paper is taken up by adverts with minimal text. You could estimate this number based on common sense /

experience, and then check with the interviewer to make sure. Given the low word density of advertisements compared to text, it would be a

reasonable approximation to discount their word contribution, and therefore assume that, of the 65 pages, 20% are non-text pages. This is

equivalent to 65 / 5 = 13 pages of adverts. This leaves 65 13 = 52 pages of news stories .

Question 3: What fraction of news story pages is taken up with images or diagrams?

In addition to adverts, news stories are often illustrated with images or diagrams that take up a large amount of space on the page. This would vary

across different sections of the paper (for example, the main News section will have more images than the Business section), so you would be

expected to take an average across the whole paper. A reasonable approximation is that 25% of news space is taken by diagrams and images.

Remembering that you have calculated that there are 52 pages excluding adverts, 0.25 x 52 pages = 13 pages of news related images and

diagrams. This leaves 52 13 = 39 text-only page equivalents .

Que s tion 4 : Wha t is the numbe r of words on a te x t-only pa ge ? One way of working out the number of words on a text page is to break it

down into (number of columns) x (number of words per column line) x (number of lines per column). From experience, you might know that a typical

compact broadsheet format like The Times has five columns of text on a page. On average, it is reasonable to expect 6 words per line in a

column . This totals 30 words across each horizontal line of page.

A guess of the number of lines down a page based on the experience of reading The Times is more difficult, so you might want to compare it to a

more familiar paper size, such as an A4 sheet. You might estimate that the length of a compact broadsheet is equal to roughly 1.5 A4 sheets

(whereas a traditional broadsheet is over 2 times longer than an A4 sheet). Wide ruled A4 paper has about 35 lines per page so 1.5 wide-ruled A4

pages would hold 52.5 lines you could round this to 50 to make later calculations easier. You would also want to take into account the fact that

newspapers typically use much smaller type fonts than hand-writing, allowing them to fit more lines to the page. Assuming that newspaper line

spacing is about half that of wide ruled A4, a typical newspaper may have 2 x 50 = 100 lines per page. This would make 100 lines * 30

horizontal words = 3000 words per page.

An extra step to the analysis would be to account for the space taken up by he a dline s, which typically take up around 1/3rd of the page. Accounting

for headlines, the number of words on would be 2/3 x 3000 = 2000 words per page .

We calculated previously that there were 39 pages of text in the average copy of The Times. This implies that there are 39 x 2000 = 78 000 words in

the average copy of The Times. Given that the number of calculation steps involved, you might want to conclude by expressing your final estimate

as a range, rather than a precise number: e.g using a confidence interval of +/- 5%.

Therefore, a copy of the Times might typically contain 75,000 80,000 words .

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