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I have taken a quotation, and I have replaced each of the letters with one-, two- of three-digit numbers according to the table below. Can you change it back to letters?
Be careful though, as some sequences of numbers could lead to several words, for instance 31110 could mean CAT (3,1,110), but could equally mean MAD (31,1,10).
This particular quotation is from Leo Tolstoy.
Where in everyday life in the UK might you encounter a numerical sequence that alternately subtracts 49 or adds 50 to the previous number?
When ‘Christian festival’, ‘annoy’ and ‘childminder’ initially lurch to the right, they become ‘food tester’, ‘parent’ and ‘better adapted’.
What animal does ‘speak/complete’ become?
Insert the numbers 1 to 8 into the eight empty squares, so that the sum of the three numbers along each edge give the totals shown.
Of the 50 US states, there is one that contains all of the letters of OLD ASH, and there is one that contains none of those letters.
Find both of the states.
Draw fences between some of the posts so that each post is at the junction of exactly three fences.
These fences will divide the field into several paddocks; any paddock whose area is greater than a single triangle will contain a number, which will indicate the area of the paddock that contains it.
The boundary fence is already in place, so any post on the boundary only needs one more fence emerging from it in order to make up its full complement.
For example:
Here is the puzzle:
You have a pair of concentric circles, of diameters 187 and 119 respectively. If you draw a chord of a particular length, the points at which it goes in and out of the inner circle will divide the line exactly into 3 parts, each of length ‘x’.
What is the value of ‘x’?
What was unusual about the two 1990’s England Rugby players ‘Beal’ and ‘Back’?
You don't need any detailed knowledge of Rugby to answer this.
Where in everyday life would you find the numbers
2^(-A/2+1/4) and 2^(-A/2-1/4)
where A = 4?
There are five common words, each of which is a rearrangement of the 8 letters of LARGE TIN.
What are they?
In a new football league there are five teams: Allesley, Bannerbrook, Canley, Dunsmore and Earlsdon. Over the course of 10 weeks, each team must play every other team twice (once home and once away). There will be two games each week, with one team getting a rest. It is your job to organise the fixtures.
Is it possible to organise the fixtures so that each team alternates between home and away games?
If it is, find an example fixture list; if it is not, why not?
I’m thinking of a number.
If I was to write down all of the numbers from 1 up to and including my number, the number of digits I would write down would be exactly 4 times my number.
What is my number?
This is really quite a tough one, so I wouldn’t blame you for sitting this one out. I promise to be gentler next week!
I have invented a function of a number, let’s call it the ‘cumulative unrepetitiousness’, C(n). The function looks at all the positive whole numbers up to and including n, and splits them into two categories: into category A go all of the numbers which contain some identical consecutive digits (such as 113 or 3457335), and into category B go all of the numbers that contain no identical consecutive digits (such as 34567 of 2323). C(n) is the size of category B minus the size of category A.
The value of C(n) either goes up or down by 1 as n goes up by 1:
C(1) = 1
C(2) = 2
C(3) = 3
C(4) = 4
C(5) = 5
C(6) = 6
C(7) = 7
C(8) = 8
C(9) = 9
C(10) = 10
C(11) = 9
C(12) = 10
etc.
As you can see, for small values of n, C(n) is always positive.
When n gets big enough, C(n) is always negative.
For a brief time in the middle, C(n) crosses the zero line several times. In fact there are a total of 35 positive values of n for which C(n) = 0, before it heads off into the negative zone for ever more.
Your task is simply to find the first of these.
At my office there is often confusion created around our five-digit contract numbers. A common error involved numbers with repeated consecutive digits, for example 54467 might be wrongly written as 54667. To combat this problem it was decided that, for the contract numbers beginning with 6, no repeated consecutive digits would be allowed. So 60000 is out straight away. In fact the first acceptable number of this new scheme would be 60101.
How many of the 10000 possible numbers from 60000 to 69999 can still be used as contract numbers?
I have a bed of nails where the nails, of equal height, are arranged in a square array with 6cm between adjacent rows and 6cm between adjacent columns. I have a globe, 11cm in diameter, which I place onto the bed of nails. It settles so that it is resting on the tips of four nails.
How much higher will the top of the globe be than the tips of the nails?
I have an n-sided die. I roll it repeatedly until I've seen all of the sides at least once. The average number of throws this should take is 72.
How many sides does the die have?
A real life problem: can you fit the contents of a packet of large rice cakes (14 discs that are 10cm in diameter and 2cm thick) into a round plastic Haribo tub (internal dimensions: 20cm diameter by 10cm high)?
In the country of Brookgladia, there are only two denominations of coinage, both whole number amounts higher than 2. Using just the two values of coins it is possible to total any whole number amount from 64 upwards, however it is impossible to total 63.
What are the values of the two coins?
There is a circular park with a radius of 200m. I want to build a circular lake of radius 91m inside the park.
I wish to be able to walk from a point on the edge of the park, on a straight line tangential to the lake, until I meet the edge of the park again, and then do the same twice more and end up where I started.
If I place the lake centrally in the park, I will go past my original point on the circumference.
If I place it too far from the centre of the park, I will not get all the way round to my starting point.
How far from the centre of the park should the centre of the lake be to ensure that I end up precisely where I started?
This game uses all 100 scrabble tiles drawn at random, including the two blanks (which can represent any letter of your choosing).
The scoring system is the same as that of real ten-pin bowling: you get points for each word, equal to how many letters in the word.
In addition, there are bonus points available as follows:
If you get a spare (use all letters in one frame using two words), you get bonus points equal to the next word you score.
If you get a strike (a ten letter word), you get bonus points equal to the next two words you score.
If you only get one word in a frame, and it's not a strike, then for the purposes of bonus points, you get a zero length word too.
In real tenpin bowling, if you get a strike or a spare on the tenth frame, you get an eleventh frame to determine your bonus points, and if you were lucky enough to get a strike on the tenth and eleventh frames, you would get a twelfth frame.
In this game, there are no eleventh and twelfth frame, so to determine any bonus points you are entitled to after the tenth frame, look back at the words you scored in the first and second frames.
Theoretical maximum points is 300 (for 10 strikes), but anything over 100 is respectable. I’ve no idea what is the most points achievable with this selection, and will be playing along with everyone else!
