Home » maths » Two volumes of Pushkin [math problem]

Two volumes of Pushkin [math problem]

Two volumes of Pushkin, the first and the second, are side-by-side on
a bookshelf. The pages of each volume are 2 cm thick, and the cover – front
and back each – is 2 mm. A bookworm has gnawed through (perpendicular to
the pages) from the first page of volume 1 to the last page of volume 2. How
long is the bookworm’s track?

[This topological problem with an incredible answer – 4 mm – is absolutely
impossible for academicians, but some preschoolers handle it with ease.]

Then the author of the problem 13 writes at the end:

I tried to illustrate with this problem the difference in approaches to tasks by mathematicians and physicists, in my invited paper in the journal “Physics – Uspekhi” for the 2000 Christmas jubilee. My success surpassed by far what I intended: the editors, unlike preschoolers, on whom I had been basing my experience, failed to solve the problem, and therefore altered it to match my 4mm answer as follows: instead of from the first page of volume 1 to the last page of volume 2″ they typeset from the last page of volume 1 to the rst page of volume 2. This true story is so implausible that I am including it here: the proof is the editors’ version published by the journal.

If you still can’t figure out why that holds and the “obvious” answer is incorrect, then as hint: the first book is on the left and the second book is on the right.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: