geometry - Hexominoes into 7 simultaneous congruent shapes

I came up with this puzzle 16 years ago, it was on Ed Pegg's Mathpuzzle site but nobody solved it AFAIK. The 35 hexominoes (which look like this): are to be arranged, in groups of five, into seven shapes congruent to this one.

The sample above is not a useful shortcut, if you start like this you won't be able to do all seven. In theory you could do this without a computer. In practice... I couldn't.

Answer

The 35 hexominos can be tiled like this:

How did I find the tiling?

At first, I tried to find a solution without computer. I created the hexominoes in a graphics program and played with them. I could get up to five of the shapes filled, but for the last remaining shapes, I ended up with final gaps that required hexominoes that were already in use.

I then resorted to a computer approach. First, I determined which sets of five hexominoes can fill the given shape. Out of the C(35, 5) = 324,632 possible sets, only 2,664 can tile the given shape.

Then I tried to find an exact cover of these sets. I hope I haven't made a mistake, but my program tells me that the distribution above is the only one that solves the problem.

The exact tiling is a by-product of the first step, but I tiled the shapes by hand again — it's relaxing.