Solutions (And New Problems)

Solutions to my .last set of problems and a new set. Also some photographs.

INTRODUCTION

It has been a few days since my last post, and the principal reason for this will made clear in my next post. Meantime I am starting proceedings for today by answering the questions I included in my previous post, and then setting a couple of new ones.

SOLUTION 1 – TRIANGLE CENTERS

Here is the original problem, from brilliant:

triprob

Here is the answer:

TriAnswer

To explain, here is Alex Warneke’s published solution (one of a number, but the one I like best)

Draw a circle around each figure. The circle drawn around each polygon has a larger circumference than the polygon and therefore a larger radius than the circle. If we consider the ratio of circumference of a circle to perimeter of inscribed regular n-gon we see it is bigger for smaller n and smallest for n = 3.

SOLUTION 2: EBBINGHAUS DISILLUSION

This was the problem:

Ebbinghaus

The two blue circles are exactly the same size. Here is an edited version of the above, deliberately clumsy so that my method of editing it can be seen by all:

Ebbinghaus Disillusion

PROBLEM 1: DECK OF CARDS

The first of two new problems from brilliant that I am sharing in this post:

Card problem

This is a multi-choice question, the possible answers being:

a) Less than 50%
b) More than 50%
c) Exactly 50%

PROBLEM 2: GROYNE

Again from brilliant:

Groyne Q

As the title of this section indicates I have identified a clear-cut mistake in the wording of the question – there may be room for doubt as to whether the indicated structure is a groyne or a jetty, but it is most definitely not a ‘breakwater’ – such would be entirely out at sea, not stretching from the land into the sea. 

PHOTOGRAPHS

MinsterMajestic Clock TurretGreyfriars Tower