Triangle Game

Topic: Logic

Difficulty: 7/10

Hint in 3…..

 

2………

 

1………

 

From the top circle, label each circle (a to f) in a clockwise manner.

The edges(a,c,e) are used twice while the middle numbers are used only once.

 

 

 

 

Solution in 3…..

 

2………

 

1………

 

 

FULL SOLUTION

Step 1: Add the sum of the 3 sides and you will get
(a+b+c) + (c+d+e) + (e+f+a) = (a+b+c+d+e+f) + (a+c+e)

Step 2: We know that (a+b+c+d+e+f) = 21(Sum of 1 to 6)

Step 3: Since the sum of each side must be equal, we know that
21+ (a+c+e) must be divisible by 3.

Step 4: Since 21 is divisible by 3, (a+c+e) must also be divisible by 3.

Step 5: The sum (a+c+e) ranges between 6(1+2+3) & 15(4+5+6).
Listing down the possible values we get: 6,9,12 &15.
So we conclude that there are 4 possible sum along the sides