Introduction - A Mind reading game!!

    Consider two friends namely Ram and Deepak. Ram is a clever boy who is always interested in solving puzzles.

    Once he asked Deepak to think of a number, multiply it by 3 and add 6 to the product. Then he asks Deepak to say the result. Deepak said 21. Ram guessed correctly the number that Deepak had thought of is 5. Deepak is surprised.  

     Ram then asked him another similar puzzle in which he asked Deepak to multiply 4 to any number he has in his mind and subtract 2 from the product. Deepak says the result is 30. Ram declared that number to be 8. It is right this time too.

   This chapter would help you to know the technique that Ram has been using to solve such mind reading games very easily.

Source: Bhargavi Ramani, 12 June 2013, Text Section, Simple puzzles for clear idea on how equations are used.

Setting up of an equation

Now we will solve the above mentioned puzzles:

Puzzle I:

 The number in Deepak’s mind could be anything. Let’s represent it with some letter ‘x’,

When multiplied by 3 => it becomes 3x;

When 6 is added to it => it becomes 3x + 6;

This value (3x + 6) varies as the value of x varies.

When x=1; then 3x+6 = (3*1) +6 = 3+6 = 9

When x=2; then 3x+6 = (3*2) +6= 6+6 = 12

When x=3; then 3x+6 = (3*3) +6= 9+6 = 15

When x=4; then 3x+6 = (3*4) +6= 12+6 = 18

When x=5; then 3x+6 = (3*5) +6= 15+6 = 21

This proves that the number Deepak had in his mind is 5 and Ram’s guess is right.

The value of x can be found by solving the equation,

3x + 6 = 21--------- (I)

Puzzle II:

Let the number is Deepak’s mind is denoted by letter ‘y’,

When multiplied by 4 => it becomes 4y

When 2 is subtracted from it => it becomes 4y-2

As Ram guessed, by substituting ‘8’ in place of y, the expression (4y-2) becomes

4y-2 = (4*8)-2 = 32-2 = 30

The value of y can be found by solving the equation,

4y-2 = 30---------- (II)

Source: Bhargavi Ramani, 12 June 2013, Text Section, Formation of equations for above puzzles.