Problem
The top face of the top die shows 2. Its bottom face is the opposite face, so it must make 7 with it.
On a real die the face directly opposite the one you see is fixed by the partner rule, so once I see 2 on top I instantly know 5 is underneath.
6.G.A.4Create A Physical RepresentationThe bottom face of the top die shows 5.
Two faces on opposite sides of a die always add to 7, and the top shows 2, so the face directly beneath it has to make up the rest.
Top and bottom really are one of those opposite pairs, because a cube's six faces pair off into three couples that face away from each other.
The bottom of the top die (5) touches the top of the middle die, and a touching pair sums to 8. So the middle die's top face is 8 - 5.
The touching rule is a 'fill in the missing number' fact: 5 + ? = 8, so the hidden touching face must be 3.
1.OA.D.8Draw A DiagramThe middle die's top is 3, so its opposite bottom face makes 7 with it.
Same partner rule one cube lower: the face under 3 on the same die is 4.
6.G.A.4Create A Physical RepresentationThe bottom of the middle die (4) touches the top of the bottom die, and a touching pair sums to 8. So the bottom die's top face is 8 - 4.
Again 4 + ? = 8, so the touching face on the lowest die shows 4.
1.OA.D.8Draw A DiagramThe bottom die's top is 4, so the face resting on the ground is the opposite face, making 7 with it.
Reading the tower top-to-bottom (2, 5 | 3, 4 | 4, ?) every step obeys both rules, so the ground face is the 3 that completes 4's partner.
6.G.A.4Guess And CheckClimb down the dice tower one face at a time: 'opposite makes 7' flips a face, 'touching makes 8' hops to the next die.