1. A pleasant surprise
When I worked on the diameter problem for d-polytopes with n facets. I was aiming to prove an upper bound of the form but my proof only gave
It was a pleasant surprise to note that .
2. A bigger surprise
A few weeks ago James Lee gave a talk and proved a bound of the form I was surprised to learn from him that
(Update: I got it wrong at first, thanks guys)
This is an even more surprising special case of the formula above.
3. Is it better to have the discount first?
Question: What is a better deal: A store that gives 12% student-discount after it adds a 12% value added tax to the price of the product? Or a store that first adds 12% tax on the entire sum and only then deducts 12% student discount?
Ohh, The way I asked this question the two alternatives are precisely the same. Let me ask it again: What is a better deal: A store that gives 12% student discount after adding a 12% value added tax to the price of the product? Or a store that first deducts the 12% student discount, and only then adds 12% tax on the new price?
Answer: The same, by a surprisingly not obvious special case of commutativity of multiplication.
(See a related comment on Dave Bacon blog.)