INTRODUCTION

I have five puzzles to share (all via the mathematical website Brilliant – I am approaching a double century, my current solving streak now extending to 199 days) and photos that I have categorized in four groups. Therefore I will be interleaving puzzles and pictures.

PUZZLE 1: LOGIC

This is an easy one – Lestrade would probably solve it without amateur assistance!

PHOTOGRAPHS 1 – CAIRINA MOSCHATA

In preparation for the Christmas Day festivities I went for a walk yesterday morning, and many of the photos you will see were taken during that walk – others were taken at other times of the day. I first came across these birds when they were in a group near Kettlewell Lane, and since then I have seen a single specimen, in The Walks, on three separate occasions, most recently yesterday:

PUZZLES 2: AN AREA CHALLENGE

This one should not be too difficult either:

PHOTOGRAPHS 2: BUILDINGS

When everything is closed the opportunity is there to get unimpeded pictures of buildings that are usually busy.

PUZZLE 3: EVEN AND ODD

This is one is tricky rather than difficult per se – and only 37% of solvers on Brilliant managed to crack it:

PHOTOGRAPHS 3: LOCAL HISTORY

Recent renovations in the building that my aunt’s house is part of have revealed some very interesting little details, and I also got some interesting shots from the house of the person with whom we had Christmas lunch.

PUZZLE 4: A DIVISABILITY TEST

Not at all difficult, but very enjoyable to tackle:

PHOTOGRAPHS 4: WILDLIFE

We finish our photographs as we started, with a nod to nature:

PUZZLE 5: THE INVESTMENT EXPERT

We end with a fairly tough problem to which I have added an even tougher subsidiary question.

My follow up, adapted from a question raised by someone named Anne on Brilliant is this: What is the minimum initial deposit required to ensure that Fred’s money grows at a sufficient rate for him to become a trillionaire if he lives for as long as Earth remains an inhabitable planet (the increasing size and temperature of the sun will cause this in 1 billion years, assuming that some stupid species has not already done so,