Here's this week's collection. Answers & extensions here. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit.

#### Two

Find

*a*such that*a*+(*a*+*A*)^{-1}= 2, where*A*= (*a*+*A*)^{-1}.ie.

*a*+ /(*a*+1/(*a*+1/(*a*+1/(*a*+1/(*a*+1/(*a*+...)))))) = 2.Find

*b*such that*b*+(*b*+*B*)^{0.5}= 2, where*B*= (*b*+*B*)^{0.5}.ie.

*b*+ √(*b*+√(*b*+√(*b*+√(*b*+√(*b*+√(*b*+...)))))) = 2.Find

*c*such that*c*+(*c*+*C*)^{2}= 2, where*C*= (*c*+*C*)^{2}.In terms of

*k*, find*d*such that*d*+(*d*+*D*)^{k}= 2, where*D*= (*d*+*D*)^{k}.#### Reverse Bases Again

Find three digits

*a*,*b*and*c*such that*abc*in base 10 is equal to*cba*in base 9?#### Adding bases

Let

*a*_{b}denote*a*in base*b*.Find bases

*A*,*B*and*C*less than 10 such that 12_{A}+34_{B}=56_{C}#### Complex Squares

For which complex numbers,

*z*, are Re(*z*^{2}) and Im(*z*^{2}) both positive?#### Rebounds

In a 4x3 rectangle, a ball is fired from the top left corner at 45°.

It bounces around a rectangle until it hits a corner. Which corner does it end in?

Which corner will it end in for rectangles of other sizes?

Did you mean something slightly different for complex squares? You've written Re(z^2) twice.

ReplyDeleteYes I meant Re and Im. It's changed now

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