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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

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

HEDGEHOGHow many spikes are there on the back of a hedgehog?

Answering this question requires answering a number of sub-questions (SQ):

Question 1: How do you define the 'back' of a hedgehog?

Possible solutions:

Could define this as the whole area upon which spikes can be found

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Could be the whole area that is not in contact with the ground

Could be an area in a similar proportion to the circumference of the hedgehog (when viewed from above) but of smaller size i.e. the area aroundit can be described as the sides rather than the back

Let's go with the latter option and try to determine the area of that

Question 2: What is the area of the back?

Estimating the size/shape of a hedgehog, you could say it could be held comfortably in your hands:

Ellipsoid in shape so Elliptic when viewed from above

20cm in length

16cm in width

Assuming that the curvature of the hedgehog is 'smooth' between the back and sides and so the back ends and side starts halfway betweencentre and outside of the ellipse:

the length of the back is 10cm (radius L = 5cm)

the wide of the back is 8cm (radius W = 4cm)

For simplicity, assume the surface area of the back when flattened is of similar size

Using the standard formulae for the area of an ellipse, the area of the back of the hedgehog = Pi * radius L * radius W = 3.14 * 5 * 4 ~= 63 cm2

Question 3: How many spikes are in a specific area of the back?

Let's consider an area of 1cm2as the specific area

Spikes are much thinker than human hairs so let's assume that the width of a spike is 1mm

Assuming that the spikes are packed together and each takes up an area of about 1mm2, then the total number of spikes in 1cm2 is 100

Final Step: How many spikes are there on the back of a hedgehog?

Let's assume that the density of spikes is uniform across the back

Given a total area of 63cm2on the back and 100 spikes within each 1cm2, the total number of spikes is approximately 6,300

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