3 regular die are placed adjacent to each other in a row. The long face is facing you and you see the dots. Starting from the left, you see dots 

1 on the left, 4 facing you and 5 on the top of the dice
For the middle die, you can only see 3 dots facing you and 6 on top
For the right most die, you can only see 6 facing you and 2 on top

Q1: How many sides can’t you see?
Q2: what is the sum of the dots on the hidden sides?

### Solution Overview:
Each regular die has 6 sides, but in the setup described, some sides are hidden. For each die, we'll determine which sides are visible and which ones are hidden. Then, we'll calculate the sum of the dots on the hidden sides.

### Breakdown for each die:

#### Leftmost die:
- **Visible sides**: 
  - Left side: 1
  - Front (facing you): 4
  - Top: 5
- **Hidden sides**: 
  - Right side
  - Back
  - Bottom
  - Since the total of all numbers on a die is 21 (sum of 1 to 6), the sum of hidden sides is:  
    \[
    \text{Hidden sum for left die} = 21 - (1 + 4 + 5) = 21 - 10 = 11
    \]

#### Middle die:
- **Visible sides**: 
  - Front (facing you): 3
  - Top: 6
- **Hidden sides**: 
  - Left side
  - Right side
  - Back
  - Bottom
  - The sum of hidden sides is:  
    \[
    \text{Hidden sum for middle die} = 21 - (3 + 6) = 21 - 9 = 12
    \]

#### Rightmost die:
- **Visible sides**: 
  - Front (facing you): 6
  - Top: 2
- **Hidden sides**: 
  - Left side
  - Back
  - Bottom
  - The sum of hidden sides is:  
    \[
    \text{Hidden sum for right die} = 21 - (6 + 2) = 21 - 8 = 13
    \]

### Answers:

#### Q1: How many sides can’t you see?
Each die has 6 sides, and for the left and right dice, you can see 3 sides (front, top, and one adjacent side), while for the middle die, you can only see 2 sides (front and top). 

- For the left and right dice, 3 sides are hidden.
- For the middle die, 4 sides are hidden.

Thus, the total number of hidden sides is:
\[
3 + 4 + 3 = 10 \text{ sides}
\]

#### Q2: What is the sum of the dots on the hidden sides?
From the calculations above:
- Sum of hidden dots for the left die = 11
- Sum of hidden dots for the middle die = 12
- Sum of hidden dots for the right die = 13

Thus, the total sum of the dots on the hidden sides is:
\[
11 + 12 + 13 = 36
\]

### Final Answers:
- **Q1**: The total number of hidden sides is **10**.
- **Q2**: The sum of the dots on the hidden sides is **36**.

Would you like any further clarifications or details on these calculations?

### Related Questions:
1. What is the total sum of dots on all visible faces?
2. If the rightmost die had 3 dots on top instead of 2, what would be the new sum of hidden dots?
3. What is the maximum possible sum of dots on the hidden sides for all three dice?
4. How would the sum of hidden dots change if the middle die showed 4 dots facing you?
5. If the dice were stacked instead of placed in a row, how many sides would be hidden?

### Tip:
The sum of numbers on opposite faces of a die always equals 7. This can help in solving similar problems more quickly!

3 regular die are placed adjacent to each other in a row. The long face is facing you and you see the dots. Starting from the left, you see dots: 1 on the left, 4 facing you and 5 on the top of the dice. For the middle die, you can only see 3 dots facing you and 6 on top. For the right most die, you can only see 6 facing you and 2 on top. Q1: How many sides can’t you see? Q2: What is the sum of the dots on the hidden sides?

Explore a math problem involving three regular dice placed in a row. Learn how to calculate the number of hidden sides and the sum of dots on the hidden sides. A great exercise in combinatorics and 3D geometry, suitable for students in Grades 6-8.

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