Math Quiz History

This page relates to the questions posed in MathQuizOne.

Q1: What number is the first blank in the well-known sequence below?

60, blank, blank, 120, blank, blank, 140, 144, blank, 150, ...

A1: The answer is 90. The numbers are generated by 180 - 360/n (where n takes the successive integer values 3, 4, 5, ...)

Q2: Why is the sequence "well-known"?

A2: Consider the simple regular polygons with n sides, where n = 3, 4, 5, etc. The number of degrees in the interior angle at a vertex is given by 180 - 360/n.

Some notes from solvers:

Interesting challenge: how to communicate that you know without passing along valuable clues. Hm... It involves something that you can do at the dinner table if you have enough silverware. --DaveSmith

This is actually a topic in information theory, called Zero Knowledge Interactive Proof Systems. -- UncleMatt

The classic solution is to code the answer in an anagram, like: "The angels of regal Ulys' pogon". Today, we just give out a crypto hash of the correct answer. -- StephanHouben

It seems harder to give an good unhelpful hint than to solve the problem. Here's a pretty obscure one. (two levels of indirection) Teaspoon of water... -- MatthewWilbert (This was intended to be decoded as TSPH2O, and then to Triangle,Square,Pentagon,Hexagon,Heptagon,Octagon.)

[Fair enough - but one level really - I had thought you were hinting at "n" as well ('an good' instead of 'a good') -- vk]

For this type of answer, the subtlest hint that you've figured it out correctly suffices -- VickiKerr [Get it?]

One of the tricky parts of Q2 is that not all of the blanks are integers, but since the problem involves a sequence, you are lulled into thinking that they are.