![Mathematics Activity]](images/headings/activity_head.gif)
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 have been 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.
In the 2011 Euler Teacher notes, Problem 6 solutions, there is an error in the formula for P(n), The upshot
is that the solution n=1 should be removed. The values of P(n) are incorrect but
the remaining list for n remains correct, as does the solution method and mark scheme.
In the 2011 Euler Teacher notes, Problem 10 solutions, the solution is incorrect.
Teachers, to obtain the correct solution, please email here using
your school email address. We are emailing the correct solution to participating schools.
The correct solution lends itself to the mark scheme in the teacher reference notes.
Sample Problems and Solutions
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