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In this problem, we have two blocks with initial temperatures:
- **Block 1**: 68°C
- **Block 2**: 176°C

Since no energy escapes, the system is closed, which means the total energy (and therefore the average temperature) of the two blocks will remain constant. We can calculate the initial average temperature to determine the possible final temperatures.

### Step 1: Calculate the Initial Average Temperature
The average temperature of the two blocks initially is:
\[
\text{Average Temperature} = \frac{68 + 176}{2} = \frac{244}{2} = 122^\circ \text{C}
\]

### Step 2: Determine the Possible Pair of Temperatures
After some time, energy can be transferred between the blocks, but the total energy remains the same, meaning the average temperature must still be 122°C. Therefore, any valid final pair of temperatures must average out to 122°C.

Let's check each option:

1. **104°C and 212°C**
   \[
   \frac{104 + 212}{2} = \frac{316}{2} = 158^\circ \text{C} \quad (\text{not 122°C})
   \]

2. **68°C and 146°C**
   \[
   \frac{68 + 146}{2} = \frac{214}{2} = 107^\circ \text{C} \quad (\text{not 122°C})
   \]

3. **120°C and 124°C**
   \[
   \frac{120 + 124}{2} = \frac{244}{2} = 122^\circ \text{C} \quad (\text{valid})
   \]

4. **174°C and 70°C**
   \[
   \frac{174 + 70}{2} = \frac{244}{2} = 122^\circ \text{C} \quad (\text{valid})
   \]

Thus, both pairs **120°C & 124°C** and **174°C & 70°C** are possible.

### Answer:
The correct answer includes both options **120°C & 124°C** and **174°C & 70°C**,

Later, the temperature of each block is measured again. Which pair of temperatures is possible?

Learn how to determine the possible final temperatures of two blocks in a closed system using average temperature. This problem involves the conservation of energy, requiring that the average temperature remains constant at 122°C. Suitable for students in Grades 6-8.

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