Five students each wrote a number on a piece of paper. The numbers could only be 1 or 2 or 4. What could be the product of the five numbers written?
(a) 100
(b) 120
(c) 256
(d) 768
(e) 2048
The correct answer is (c).

If all the students wrote the number 1, the product would be 1, which is not among the options. Therefore, 2 or 4 are factors of the product, and thus the product must be a power of 2. The largest possible product would be obtained if all 5 students wrote the number 4, and the product would be

$$
4 \times 4 \times 4 \times 4 \times 4=4^{5}=2^{10}=1024
$$

Therefore, we can eliminate 2048. Now we have:

- 100 and 120 are divisible by 5, so they are not powers of 2;
- 768 is divisible by 3 (7+6+8=21), so it is not a power of 2.

The only possible answer is $256=2^{8}$. For example, this would be the case if two students wrote the number 2 and three wrote the number 4, with $256=2 \times 2 \times 4 \times 4 \times 4$.