## Apr 13, 2010

### Mathematics Challenge for Young Australians: Enrichment Stage

http://www.amt.edu.au/wuenr.html

#### Mathematics Challenge for Young Australians: Enrichment Stage

This page is designed to give students an alternative problem set to this year's formal Enrichment Problems, together with solutions. This may help students see what is expected in solutions. Students are encouraged to try solving without seeing the solutions, but in any case the solutions are provided to enable students to see what is expected.

This page contains a recent problem set for each of Newton, Dirichlet, Euler, Gauss, Noether and Polya.

#### Errata

In Newton Student Notes the solution to Problem 19, Chapter 5 is 18 faces, 16 vertices and 32 edges. Euler's Rule is satisfied as 18+16-32=2.

In chapter 8 (Solutions, question 1), 7308 is actually divisible by 3 and 9 whereas the recent reprint gives it as No for both.

The Dirichlet Student Notes are being reprinted, with some reorganisation of text (not affecting the chapter problems). For those with the 2006 printing though, there are some errata:

In the table on page 7, the N in column 3 against deep sea diver should drop to the journalist row. In the upper table on page 8 the Ns against deep sea diver and journalist should swap places.

In the two dot points at bottom of page 42: The number of squares should be s=1+2(n-1)=2n-1. And the number of match sticks should be m=4+3.2(n-1)=6n-2.

In both tables on page 51 columns 3 and 4 should be empty.

Further there are three incorrect solutions in Chapter 3. For Problem 7 the correct answer is 513, for Problem 9 the correct answer is 1432 and for Problem 11 the correct answer is 94. The answer to Problem 11 is just 11 and the answer to 40 (d) should be 2737. For Chapter 8, Problem 20 the solution should have a bar over 73170.

Noether Problem 15 would be better worded as "Does there exist a positive integer such that when it is written in base ten and its leftmost digit is crossed out, the derived number is one-fifty-sixth of the original number?"

Sample Problems and Solutions