Placing the Numbers | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Place the numbers 1, 2, 3, 4, 5, 6, 7, 8 into the eight circles in figure given below, in such a way that no number is adjacent to a number that is next to it in the sequence. For example 1 should not be adjacent to 2 but can be adjacent to 3, 4, 5, 6, 7, 8. Similarly for others.

The Easiest Numbers to Place

The numbers 1 and 8 are the easiest to place because they each have only one number to which they cannot be adjacent. 1 cannot be next to 2, and 8 cannot be next to 7.

The Hardest Circles to Fill

The middle circles are the hardest to fill because each one is adjacent to six other circles.

Placing 1 and 8 in the Middle Circles

To make things easier, we can place 1 and 8 in the middle circles. If we put 1 to the left of 8, then the only possible positions for 2 and 7 are the two end circles.

Placing 3 and 6

Next, we can place the numbers 3 and 6. The number 3 must be placed on the left-hand side of the diagram, and 6 must be placed on the right-hand side.

Placing the Remaining Numbers

With only four numbers left to place, it becomes easy to fill in the remaining circles. Simply place 2 and 4 in the left-hand side of the diagram and 5 and 7 in the right-hand side of the diagram.

In summary, by strategically placing 1 and 8 in the middle circles, we can easily solve the puzzle of placing the numbers 1-8 in eight circles without any adjacent numbers in the sequence.