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

#### Two Lines

Let A and B be two straight lines such that the gradient of A is the

*y*-intercept of B and the*y*-intercept of A is the gradient of B (the gradient and*y*-intercept of A are not the same). What are the co-ordinates of the point where the lines meet?#### Odd Sums

What is (1+3) ÷ (5+7)?

What is (1+3+5) ÷ (7+9+11)?

What is (1+3+5+7) ÷ (9+11+13+15)?

What is (1+3+5+7+9) ÷ (11+13+15+17+19)?

What is (sum of the first

*n*odd numbers) ÷ (sum of the next*n*odd numbers)?*x*^{xxxxx...} Again

Let

*y*=*x*^{xxxxx...}[x to the power of (x to the power of (x to the power of (x to the power of (...)))) with an infinite number of*x*s]. What is^{dy}/_{dx}?#### Folding Tube Maps

Back in 2012, I posted instructions for folding a tetrahedron from tube maps. When tube maps are used, the sides of the tetrahedron are not quite equal. What ratio would the rectangular maps need to be in to give a regular tetrahedron?

## No comments:

## Post a Comment