![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 the 2010 Newton Teacher Reference Notes, Problem 2 lists
a certain number of hexonimoes which are needed
for a full score. In fact there is a further one for (a) which is not listed. However full marks
still apply if a student finds the same number of hexonimoes as in the Teacher Reference Notes.
In the 2010 Dirichlet Teacher Reference Notes Problem 8b, the fifth fraction listed in the solutions is in fact the sixth largest. The correct fifth largest cycle starts with the digit that is 1 more than the sixth largest cycle and its numerator is 3 more than the numerator for the sixth largest fraction.
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 9 solution lists a number 3 as one of the answers. This answer is incorrect and should be excluded.
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
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