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?

We are given three dice with specific faces visible, and we need to determine:

1. How many sides are not visible.
2. The sum of the dots on the hidden sides.

### Step-by-Step Breakdown:

#### Dice 1 (Leftmost)
- **Visible sides**: 
  - 1 (left side)
  - 4 (front side)
  - 5 (top side)
  
  A standard die has six faces, and opposite faces on a die sum to 7. The hidden faces are the opposite sides of these visible faces.
  
  - The opposite of **1** (left) is **6** (hidden).
  - The opposite of **4** (front) is **3** (hidden).
  - The opposite of **5** (top) is **2** (hidden).
  
  **Hidden sides for Dice 1**: 6, 3, 2.

#### Dice 2 (Middle)
- **Visible sides**:
  - 3 (front side)
  - 6 (top side)
  
  Here, we have two visible sides, so four faces remain hidden.
  
  - The opposite of **3** (front) is **4** (hidden).
  - The opposite of **6** (top) is **1** (hidden).
  
  Since we don't see the left, right, or back sides of this die, those sides must be hidden.
  
  **Hidden sides for Dice 2**: 1, 4, 5, 2.

#### Dice 3 (Rightmost)
- **Visible sides**:
  - 6 (front side)
  - 2 (top side)
  
  Similar to Dice 2, four faces remain hidden.
  
  - The opposite of **6** (front) is **1** (hidden).
  - The opposite of **2** (top) is **5** (hidden).
  
  **Hidden sides for Dice 3**: 1, 5, 3, 4.

### Q1: How many sides can’t you see?
Each die has 6 sides. For Dice 1, we can see 3 sides (left, front, top), so 3 sides are hidden. For Dice 2 and Dice 3, we see 2 sides (front and top), so 4 sides are hidden for each.

Thus, the total number of hidden sides is:
\[
3 + 4 + 4 = 11 \text{ hidden sides.}
\]

### Q2: What is the sum of the dots on the hidden sides?
Now, we sum up the dots on the hidden sides for each die:

- **Dice 1**: 6 (left), 3 (back), 2 (right)
- **Dice 2**: 1 (left), 4 (back), 5 (right), 2 (bottom)
- **Dice 3**: 1 (left), 5 (back), 3 (right), 4 (bottom)

Summing these hidden dots:
\[
(6 + 3 + 2) + (1 + 4 + 5 + 2) + (1 + 5 + 3 + 4) = 11 + 12 + 13 = 36.
\]

### Final Answers:
- **Q1**: There are **11 hidden sides**.
- **Q2**: The sum of the dots on the hidden sides is **36**.

Would you like more details on any of the steps or have further questions?

### Related Questions:
1. What is the sum of dots on all visible sides?
2. How would the result change if the top numbers were different?
3. What if we could only see the top faces of all dice?
4. How many total dots are on a standard die, and what percentage of those are hidden here?
5. Can we predict hidden sums for any arrangement of dice based on symmetry?

**Tip**: The sum of the opposite faces on a standard die is always 7, which helps quickly determine the hidden numbers!

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 how to calculate the number of hidden sides and the sum of dots on the hidden faces for three regular dice arranged in a row. This problem involves dice properties, using the rule that opposite faces on a die sum to 7. Suitable for students in Grades 5-7.

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