the other side of the dice
A simple riddle from the Riddler: if a standard fair six-faced dice is falling on an edge rather than a face, what is the expectation of the sum of the faces sharing this edge?
The solution proposed there is however somewhat convoluted, when the average is simply
since the only face that does not share an edge with face i is 7-i…
Xi'an's Og 
August 22, 2022 at 1:45 pm
The pictured dice isn’t a standard one to opposite faces do not sum to 7.
You have to ignore the picture to solve the riddle…
August 19, 2022 at 10:34 pm
I thought for a moment that this was a classic 3D perception problem: that cutout diagram doesn’t look like a standard six-sided die. I always thought that opposite sides always sum to the same number (7). But maybe I’m incorrect.
August 23, 2022 at 8:41 am
I did not pay attention (enough) to the picture, which indeed does not depict a standard dice.
August 19, 2022 at 9:35 pm
Do you really need the assumption that opposite faces are $i$ and $7-i$ though?
August 23, 2022 at 8:40 am
No, indeed, you do not, as the sum of the missing/opposite faces is again 1+2+..+6.