Saturday, January 12, 2013

A Cheeky Little Number

Part One

If you want to be good at number puzzles you need to understand numbers. A simple enough statement you might think, but I don't mean understanding mathematics - thats a whole different ball game. What we're looking at here is the distinct personality of numbers. 

Thinking back to our Christmas Pudding puzzle, we looked at the number 27, I said at the time it was a funny number to choose, now I want to show you why.

When I see 27 I always think of 3 x 9, it's the only way to make 27 by multiplying two numbers besides the arbitrary 1 x 27. Ending in a 7 it looks like it should be a prime number, so near yet so far. Indeed 17, 37, 47 and 67 are all prime, 27 is the lowest positive integer ending in a 7 that isn't prime.

27 does some interesting things related to cubing; obviously it's a perfect cube itself being the result of 3 cubed. Also if you find the cube of 27, you get 19,683 which, if you all all the digits together, comes to 27.

While we're adding digits, if you add all the digits between 2 and 7 inclusive you get 27.

Of course that's just in the field of arithmetic, 27 is the atomic number of cobalt, Uranus has 27 moons and there are 27 signs in the Indian zodiac. Not to mention 27 bones in the human hand and 27 States in the European Union.

Oh and don't forget 1544, that's the number of words on Wikipedia dedicated to the number 27, and if I'm honest 27 is quite a dull number.

You'd have to be a bit of a geek to sit and read the wikipedia page for the number 27 or plan three posts ago what number you were going to use for 'A Cheeky Little Number', ahem, but that's not really the point of all this. The idea is to get comfortable with numbers and how they fit together, just like we did with letters.

So here's an activity, rather than a puzzle, to get your mind thinking in numbers ready for the challenges ahead.

Number Puzzles
The Four Fours

In this puzzle you are provided with four fours to use at each stage and you must use them all. Your task is to use arithmetic methods to make every number from 1 to 100. Your arithmetic must follow the usual order of operations; brackets first then powers, division, multiplication, addition, subtraction. I warn you though, some numbers will be very difficult and others may be impossible to achieve.

You may add numbers,

4 + 4 + 4 + 4 = 16

You may subtract numbers,

4 + 4 + 4 - 4 = 8

You may multiply numbers,

4 x 4 + 4 x 4 = 32

You may divide numbers,

4 x 4 / 4 x 4 = 16

You may use brackets,

(4 x 4) / (4 x 4) = 1

You can use roots and powers, but you have to make up the number you want from your four fours. If you want to square a number, you have to make the 2 first.

4 ^ (4/4) + 4 = 8

You can combine your fours together before you do anything atrithmetical to them,

44 + 44 = 88

Finally you can make use of the factorial function, which means; multiply all the positive integers from zero to this one.

(4 + 4 + 4) + 4! = 36

You must however use all four fours in achieving each number.

Good Luck with that numerical assault, and do keep puzzling!

photo credit: fdecomite via photopin cc

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