The cooler is more than wide enough to lay down 4 cans but not wide enough for 5. Cans A, B, C, D lie next to each other to form the first layer with A and D against the corners. B and C are free to move a bit.

The next layer is E in the groove between A and B, F in the groove between B and C, G in the groove between C and D.

The next layer is H along the side of the cooler above E, I and J in the next two grooves, K along the other side above G.

The final layer L, M, N along the grooves of the previous layer.

Prove: no matter where B and C are at the bottom, the cans L, M, N are equally spaced and in a straight line.