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Sunday, 21 September 2014

Sunday Afternoon Maths XXIX

Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit. This Tuesday is Maths Jam, make sure you're there!

Three Squares

The diagram shows three squares with diagonals drawn on and three angles labelled.
What is the value of $$\alpha+\beta+\gamma$$?

Equal Opportunity

Can two (six-sided) dice be weighted so that the probability of each of the numbers 2, 3, …, 12 is the same?

Double Derivative

What is
$$\frac{d}{dy}\left(\frac{dy}{dx}\right)$$
when:
(i) $$y=x$$
(ii) $$y=x^2$$
(iii) $$y=x^3$$
(iv) $$y=x^n$$
(v) $$y=e^x$$
(vi) $$y=\sin(x)$$?