Problem 1 :

CAN YOU PLACE THE NUMBERS 1-8 IN THE SQUARES BELOW SO THAT NO TWO CONSECUTIVE NUMBERS ARE NEXT TO EACH OTHER, EITHER VERTICALLY, HORIZONTALLY OR DIAGONALLY?

This is a fairly easy problem to solve, by simple trial and error. Let us see how to get to the solution quicker by moving to the next level of the meaning of the problem statement. Try solving this problem for a few seconds before proceeding further.

The problem requires you to place the numbers 1-8 in the squares so that no two consecutive numbers are next to each other, either vertically, horizontally or diagonally.

“Whack On The Head” - What does this statement mean ? How can you state it more simply ?

It means that if you place a number ‘x’ (1 <= x <= 8)  in cell A, you can place the numbers ‘x+1’ or ‘x-1’ only in cells H, G or F.

It also means that if you place a number ‘x’ (1 <= x <= 8) in cell D, you can place the numbers ‘x+1’ or ‘x-1’ only in cell F.

For most people, this rings a bell - how can you place both the numbers ‘x+1’ and ‘x-1’ in the same cell, i.e. F ?

This indicates something – you can only place either numbers 1 or 8 in the cell D.

And that solves the whole problem WITHOUT ANY TRIAL AND ERROR, even before you have started thinking of the solution – just by rephrasing the problem statement differently and in a more simpler language.

Problem 2 :

Two boats, traveling at 5 and 10 Km per hour, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide ?

(1) 1/12              (2)  1/6              (3)  ¼                     (4) 1/3

Try this problem for a while before moving forward.

A very very common attempt is to :
i) find out the time taken ‘t’ mins for the collision
ii) find out the distance covered in ‘t’ – 1 mins
iii) subtract that distance from 20 Kms. You get the answer.

CATLounge hint :
 

We have to find out how far apart are they one minute before they collide.

Whacks On The Head : What does this statement mean ? How can you rephrase the question differently ?

how far apart are they one minute before they collide.
We are talking about the “last 1 minute”, and we are talking of how far apart are they in this one last minute
-> it is the same as how far do they travel in the last 1 minute !!!

And we haven’t even started solving the problem – we were just trying to dig deeper into the problem statement itself.