Hunting for Averages Ayaansh Dhamija

How I figured it out:

The rules say the number in each box has to be the average of the 4 circles around it. But the two boxes are touching each other! That means the left box counts as a number for the right box, and the right box counts as a number for the left box.

Let's call the left box X and the right box Y.

My Equations:

For the left box X, the numbers around it are 7, 20, 2, and Y.

• $X = (7 + 20 + 2 + Y) \div 4$
• $4 \times X = 29 + Y$

For the right box Y, the numbers around it are 15, 3, 1, and X.

• $Y = (15 + 3 + 1 + X) \div 4$
• $4 \times Y = 19 + X$
• $X = (4 \times Y) - 19$

Finding the numbers:

Now I change the X in my first equation to be $(4 \times Y) - 19$.

• $4 \times ((4 \times Y) - 19) = 29 + Y$
• $(16 \times Y) - 76 = 29 + Y$

Move the Y to one side and numbers to the other side:

• $15 \times Y = 29 + 76$
• $15 \times Y = 105$
• $Y = 105 \div 15$
• $Y = 7$

Now that I know Y is 7, I can easily find X:

• $X = (4 \times 7) - 19$
• $X = 28 - 19$
• $X = 9$

My Final Answers:

• Left Box = 9
• Right Box = 7