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Many people ask similar questions about the statements of Quiz problems via our QQ helpline. As we receive questions, we will keep adding our answers here; you might find them helpful!

What does it mean to be in base *b*?

If you're unfamiliar with writing numbers in different bases, you can learn more about them online, e.g. at https://www.mathsisfun.com/numbers/bases.html.

What if I have a digit greater than 9?

That's fine! For example, if you write 8^2 = 64 in base 13, your digits will be 4 and 12, because 64 = 4*13 + 12. So the sum of the base 13 digits is 4+12 = 16.

For part (a), do we need to show that *n*(*n*+1)/2 turns is an achievable maximum (i.e. it is possible to play such that it takes that many turns)?

Nope! We are only asking you to show that the game ends after **at most** *n*(*n*+1)/2 turns. You could also make a statement like "when *n*=1, the game will end after at most 2000 turns." This is not a very helpful statement, but it is still true, and it does not imply that it is actually possible to make the game last 2000 turns; it just means the game cannot go for more than 2000 turns.

In part (d), if the widths of the buildings add up to 1, there can't be any gaps between buildings; how can any adjacent buildings *not* share a vertical edge?

You must somehow avoid having adjacent buildings. If this seems impossible, then you are probably reading the problem correctly - but it is possible! If you're still stuck, solve parts (a) through (c) first. Then ask yourself: is it true that all of the buildings in the cities you've planned share a vertical edge with a building to the left, and with a building to the right? Do your city borders (the points (0,0) and (1,0)) share a vertical edge with a building? If you find a place where the answer is "no", try to leverage that idea to solve part (d).

In part (d), does a park in between two buildings prevent them from sharing a vertical edge?

No. If two buildings both have an endpoint at (*x*,0) for some *x*, then they share a vertical edge, even if there is also a park at (*x*,0).

In 4(b) and 4(c), is the problem asking for a specific *x*_{1} and *x*_{2} that work, or all possible values of *x*_{1} and *x*_{2}?

You should describe all *x*_{1} and *x*_{2} that make it possible to design the city, not just a specific example.

Do votes carry over to the next episode, or reset after each episode?

Vote counts reset after each episode. When a voting phase begins, each contestant starts with 0 votes against them, regardless of whether they received votes in previous episodes.

Can a Pawn associate with multiple other Pawns?

Yes! Each pair of Pawns may or may not associate, and this does not depend on any of the other associations between the Pawns.