The number of dots on opposite faces of a regular die add to 7. Four regular dice are arranged as shown. Which of the following could be the sum of the number of dots hidden between the dice?
(A) 22
(B) 26
(C) 24
(D) 21
(E) 23

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-029.jpg?height=406&width=158&top_left_y=800&top_left_x=1382)
On the bottom die, the two visible faces are showing 2 dots and 4 dots.

Since the number of dots on opposite faces of this die add to 7 , then there are 5 dots on the face opposite the face having 2 dots, and 3 dots on the face opposite the face having 4 dots.

Therefore, the top face of this bottom die (which is a face that is hidden between the dice) has either 1 dot on it or it has 6 dots on it.

On the second die from the bottom, the sum of the number of dots on the top and bottom faces (the faces hidden between the dice) is 7 since the number of dots on opposite faces add to 7. (We do not need to know which faces these are, though we could determine that they must have 1 and 6 dots on them.)

Similarly, on the third die from the bottom, the sum of the number of dots on the top and bottom faces (the faces hidden between the dice) is also 7 .

Finally, the top face of the top die shows 3 dots, and so the bottom face of this die (which is a face that is hidden between the dice) contains 4 dots.

Therefore, the sum of the number of dots hidden between the dice is either $4+7+7+1=19$ or $4+7+7+6=24$.

Of these two possible answers, 24 is the only answer which appears among the five given answers.

ANSWER: (C)