A Timeless Puzzle to Challenge Your Reasoning

Fill in the Blanks!!!

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Problem 🔴

The diagram shows a heptagon with three circles on each side. Some circles already have the numbers 8 to 14 filled in, while the remaining circles need to be filled with the numbers 1 to 7. Each circle must contain one number, and the sum of the numbers in every set of three circles along a line must be the same.

Arrange the numbers!!!

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Solution 🟢

The first step is to find the sum that each set of three circles produces. Once we have obtained this sum, we can use a trial-and-error approach to fill in the blank circles.

Let’s begin.
We have integers from 1 to 14.

• Numbers 1–7 appear in exactly two of the seven lines.
• Numbers 8–14 appear in exactly one line.

When we add up the totals of all seven lines:

• Numbers 1 to 7 are counted twice (since they belong to two lines each).
• Numbers 8 to 14 are counted once (as they belong to only one line each).

This means the sum of the seven line totals equals:

Since the total for each of the seven lines is the same, the sum of the numbers in one line is:

133/ 7=19

Step 1 is complete: We now have the target sum (19) that each line must equal.

Next task: Determine how to place the numbers 1 to 7 in each line so that their total equals 19.

Let’s flatten out the hexagon.

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Note:- the first and the last empty will contain the same number.

As stated earlier, we will use a trial-and-error approach to arrange these numbers.
Let’s start from left to right:

• We need two numbers (from 1, 2, 3, 4, 5, 6, 7)…