# October Problems

It has already been a month since the September Problems were released!!! Note that we still accept submissions until 7th of October (please keep the deadline if possible; the official deadline is the last day of the month).

The October Problems can be downloaded as a pdf file here, or see below. If you have any questions or if you want clarification on the problems, feel free to email us (nzmosa@outlook.com), message us on Facebook, or leave a comment below. At the end of the month, submit your solutions to nzmosa@outlook.com

Enjoy!  Also, on the side note, good luck to everyone who submitted the Camp Selection Problems!

## JUNIOR DIVISION

Q1: We call a set of three numbers a "triplet" if we can create a triangle with sides the length of the numbers (so $${3,5,4}$$ is a triplet but $${3,4,10}$$ is not). If $$x$$ is the smallest positive integer that will form a triplet with $$3$$ and $$6$$, and $$y$$ is the largest such integer, then find the value of $$10x + y$$.
Q2: What is the least number of $$12 \times 15 \times 20$$ blocks required to make a perfect cube?

## INTERMEDIATE DIVISION

Q3: What is the last digit of $$9^{9^{2014}}$$?
Q4: How many rectangles are there in the board containing the shaded circle?

## SENIOR DIVISION

Q5: Suppose $$x$$, $$y$$ and $$z$$ are positive integers such that:
$$x + \frac{1}{y+\frac{1}{z}} = 108/53$$
What is the value of $$x+y+z$$?
Q6: $$A$$, $$B$$, $$C$$, $$D$$ and $$E$$ are consecutive vertices of a regular polygon. The lines $$AB$$ and $$ED$$ are extended to at a point $$F$$, where $$∠ BFD = 170 °$$. How many sides does the polygon have?