In a dice, 1, 2, 3 and 4 are written on the adjacent faces, in a clockwise order and 5 and 6 at the top and bottom. When three is at the top, what will be at the bottom?

From the problem description, we can map out the exact placement of all six numbers:

• Top and Bottom: 5 is at the top, and 6 is at the bottom. This means 5 is opposite to 6.
• Adjacent Sides (Clockwise Order): The numbers 1, 2, 3, and 4 wrap around the remaining four vertical faces in a continuous clockwise circle.

2. Find the Opposite Pairs

Since 1, 2, 3, and 4 form a continuous loop around the sides:

• The face opposite to 1 will be two steps away, which is 3.
• The face opposite to 2 will be two steps away, which is 4.

So, the pairs of opposite faces are:

• $5 \longleftrightarrow 6$
• $2 \longleftrightarrow 4$
• $1 \longleftrightarrow 3$

Conclusion:

Since 3 is opposite to 1, when 3 is placed at the top, its directly opposite number, 1, will be at the bottom.