Las consecuencias de la NMF para las facultades del Presidente para dirigir las relaciones internacionales

It will be important to know (or to be able to work out) the square numbers from 12_to

152_{as well as the cubes of 2,3,4,5 and 10.}

As well as this you’ll need your

multiplication and division skills. In terms of multiplication, if you have two fairly long numbers it is often easier to look at the shorter number in sections of hundreds, tens and units and then do the

multiplication in parts like this:

532 x 52

This is the same as:

532 x (50 + 2)

Using algebra we can then simplify by multiplying 532 with each number in the bracket to get:

(532 x 50) + (532 x 2)

If it’s easier to see, you can write it like this:

((532 x 5) x 10) + (532 x 2)

Remember, multiplying by 50 is as easy as multiplying by 5 and then multiplying by 10 by adding a “0” at the end.

Do each bracket individually to get:

26,600 + 1,064

Then do the sum:

27,664

There are little tricks in multiplication and division you will discover. For example in this next spell it is useful to know that dividing by 5 is the same as multiplying by 2 and then dividing by 10.

Now for the magic! This time you will perform an incredible trick for someone else. Draw out a grid like this one with 5 squares across and 5 down. Also draw in the dots.

Tell your spectator to think of any number and that for this extreme mental challenge it should be between 60 and 500. Tell them that using their number you will create an incredible gift for them that shows how much of a genius you are.

First you must take the number they give you and subtract 60. Now work out the next smallest number from this that ends with a 5 or a 0. How many do you need to subtract to get to this number? Call the amount you subtract the “remainder” and make a note of it. Now take the number you found that ends in 5 or 0 and divide it

by 5 (use the tip above) and write the answer to this in the middle square of the top row.

For example, if your spectator picked 201, subtract 60 to get 141. The next lowest number that ends in a 5 or 0 is 140. We have to subtract 1 to get there so the remainder is 1. And 140/5 = 28 so this goes in the middle square of the top row.

You should now fill in every square one by one by completing each square that is diagonally up and to the right of the one you just wrote in with the number that comes after the one you just wrote (so 28, 29, 30, 31… ). Each time you can’t move diagonally up and to the right move one square down instead. This diagram shows the order you fill squares in:

A handbook of magical mathematical tricks for you to learn

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/

• • • • • • ₂₈ • • • • r = 1

Each time you get to the edge of the grid imagine the grid connects top to bottom and left to right so that if you go off the top you come back at the bottom, and if you go off the right you come back at the left.

So the complete order you fill in the squares should be like this:

Practice by filling an empty grid with the numbers 1-25 in the right order.

When you do this with your spectator’s number, you start with the number you wrote in the middle square of the top row and count up in the same way moving from square to square. BUT when you land on a square with a dot in it, you must also add the remainder to the number you planned to put there. See if you can follow our example where the start number is 28 and the remainder is 1:

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• 17 24 1 _{8 15} 23 5 • 7 14 16 4 6 13 20 • 22 10 • 12 19 21 3 11 18 ₂₅ •₂ 9 • 45 51 28 35 42 50 32 • 35 41 43 31 33 40 47 • 50 37 • 40 46 48 30 38 45 52 • 30 36 r = 1 • 1 8 5 •₇ 4 6 • • 3 • 2 9

Do the same thing with the spectator’s number and once you have made the grid hand it back to them. Ask them if they can see where you’ve hidden their original number (in the example it was 201). They will say that they can’t see it anywhere. Then tell them that in fact their number is everywhere in the grid, get them to add the numbers in any row, or in any column or even the diagonals and they will add up to their number! Incredible! Clearly only someone with a truly magical brain could have the mental power to produce this.

One more tip to help your mental methods; if your numbers have decimals or lots of “0s” at the end you can divide or multiply by 10s and take the 10s out of a bracket to make it easier. e.g. 6000 x 5.32 = (6 x 1000) x (532 / 100) = (6 x 532) x 1000 / 100 = (6 x 532) x 10

A sequence is a set of numbers that follow a certain rule. Each number in the sequence is called a “term”. We can often create a formula that tells us what the nth term is (in other words the formula will be an equation with the letter "n" in, when we replace the "n" with "1" the equation will tell us the 1st number in the sequence, when we replace "n" with "2" the equation will tell us the 3rd number in the sequence etc.)

Here are some examples of sequences:

If we know the terms of the sequence, how would we find the formula for that sequence? Well a useful tool is to write

out the sequence and underneath each pair of numbers write the difference of those two numbers like this:

A number in the second row is the difference of the two numbers above it. Notice that in the bottom row there is only one number repeated. In this case where the repeated number is 3 we know the formula has a “3n” in it (if the repeated number was 4 it would have a “4n” in it etc.). We then try “3n” as the formula, but notice how for each term “3n” gives us the