## Puzzles and Solutions

Some solutions and some new problems/ questions. Also details a thank you card for TFL and some photos.

# INTRODUCTION

I have solutions/ answers to some problems and a few new problems for you. I was going to be blogging about my activities on Monday, Tuesday and Wednesday but that will have to wait until tomorrow now.

# SOLUTIONS 1: OPENING THE “DOOR OF DEATH”

In my post “Coming Up – A Trip To Cornwall I set this juicy little puzzle:

Each of the three filled in columns contains one large number and several smaller numbers. In each case the big number is the sum of all the smaller numbers – 6 = 3+2+1, 28 = 14 + 7 + 4 + 2 + 1 and 496 = 248 + 124 + 62 + 31 + 16 +8 + 4 + 2 + 1. In each case the smaller numbers listed below the large number turn out to be all of that number’s factors. A number that is equal to the sum of all its factors is called a perfect number. Looking closer still we that 6 = 3 x 2, 28 = 7 x 4 and 496 = 31 x 16. In each case these multiplications consist of a larger number that can be expressed in the form (2 ^ n)-1 and the smaller number is equal to 2 ^ (n-1). Further, the larger multiplier is in each case a prime number. Investigation reveals that the next prime number of the form (2 ^ n)-1 is 127, and the other multiplier must therefore by 64. Multiplying these two numbers gives 8,128. Thus the final panel will consist of 8128, with vertically below it the numbers 4064, 2032, 1016, 508, 254, 127, 64, 32, 16, 8, 4, 2 and 1. This was a tough puzzle but it would have been downright vicious had I made the door’s mechanism consist of five panels, these four and the fifth for you to work out – for a bonus can you explain why?

I also asked if anyone could identify to the real life door that I had used as the basis for the “Door of Death”. It is one of the doors to King’s Lynn Town Hall and in reality of course it is not remotely deadly (indeed barring dying of boredom during a council meeting there I can think of no risk of death anywhere in that building).

# SOLUTIONS 2: GAYWOOD RIVER QUIZ

This one appeared in my post “The Gaywood River”. The answers are below:

# NEW PROBLEMS

I have three problems for you. The first comes from Trivia Hive. Unfortunately I cannot present it to you in their format without giving away the answer, so instead I present in plain text:

In which country is Europe’s only desert located?

a)Italy
b)Greece
c)Poland
d)Spain

Puzzle number two comes by way of the twitter feed of estate agents Abbot Fox:

Can you reveal the street name?

My third and final problem comes courtesy of the mathematical website brilliant and sends you on a treasure hunt:

# A THANK YOU CARD FOR TFL

I was delighted to receive an email from campaigning organisation sumofus inviting me to sign a thank you card to TFL for having given Uber the boot. I have already shared this invitation on facebook and twitter and ‘pressed’ it to my London transport themed website. I now invite my followers here to add their names to this thank you card:

# PHOTOGRAPHS

These photographs were taken in Norwich…