Magical Calculations

 Twos, threes & fives

Think of a number. Add 4, then multiply the result by 4. Subtract 8, then divide the result by 4. Finally take away your original secret number. The answer is 2.

Think of another number.

Double it. Add 9. Subtract 3. Divide by 2. Subtract your original number. The answer is 3.

Think of any three-digit number.

Add 7. Multiply by 2.

Subtract 4, then divide the result by 2.

Subtract it from the original number you thought of.

The answer is 5.

Ninety nine

Write down any two different numbers from 1 to 9. Then reverse the two numbers.

You should have two two-digit numbers.

Subtract the smaller number from the larger one.

Take the result, reverse the digits, and add that number to the one you got when you subtracted.

The answer is 99.

For example: 72 reverses to make 27.

Subtract the smaller (27) from the larger (72): 45.

Reverse these digits to make 54.

Add this to the previous number.

The answer is 99.

Threesy does it

You can discover whether a number is a multiple of 3 just by checking whether this is true for the sum of its digits.

For example, 12,894 has 1 + 2 + 8 + 9 + 4 = 24 = 3 x 8, so 12,894 is a multiple of 3.

You don't need to do the long division in order to find this out.

You can do this even for huge numbers that your calculator could never cope with.

For example, try: 111,222,333,444,555,666,777, 888,987. Is it divisible by 3? In fact, if you're clever, you might be able to give the answer before summing the digits.

10% up then 10% down means you lose out

A worker's boss explains that in order to stay competitive he will have to cut his pay by 10% but he will allow the employee to work 10% more hours to make up for it, "so your pay will be maintained".

Afraid not! If the worker was being paid, say, £100, the 10% cut takes him down to £90. The 10% extra hours will add back on 10% of £90, which gives him £99. He is still £1 worse off. Beware percentages - you need to know what they refer to.

Never-ending squares

Square numbers (the products of numbers multiplied by themselves) and prime numbers are important and your internet security only works because the prime numbers never run out.

You can get the endless list of squares just by adding the odd numbers up: 1 = 1 x 1, 1 + 3 = 4 = 2 x 2, 1 + 3 + 5 = 9 = 3 x 3, 1 + 3 + 5 + 7 = 16 = 4 x 4 ... and this pattern never lets you down.

However, when it comes to primes, we still have to go out hunting for them, which is why at any one time there is always a world champion largest known prime.

'Mind reading' trick

Choose a single-digit number, multiply it by 9 and if the answer has two digits add them together.

Subtract 5 from what you have, giving you a number. Turn the number into a letter by the rule A = 1, B = 2 and so on. Think of a country beginning with your letter. Take the last letter of your country and think of an animal that begins with that letter. It's odds on that you have a kangaroo in Denmark.

It all adds up... to 9

1x9=09 =0+9=9

2x9=18 =1+8=9

3x9=27 =2+7=9

4x9=36 =3+6=9

5x9=45 =4+5=9

6x9=54 =5+4=9

7x9=63 =6+3=9

8x9=72 =7+2=9

10 x 9 = 90 = 9 + 0 = 9