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Amy's Dominoes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2
We had a few solutions sent in for Amy and her dominoes. First from Lyneham Primary Maths Challenge Group in Australia who wrote:

Thanks for a great problem. Both groups worked on it and we made it a corridor display to get some more kids (and parents) thinking about it.

Their work can be seen here,
Lyneham-Amy dominoes-1.doc or Lyneham-Amy dominoes-1.pdf

Bjorn from Belfry Overstrand School in England wrote the following:

I wrote down all different dominoes in order (0:0, 0:1, 0:2...6:6), I counted them all and there were 28.
It told me that Amy had four dominoes missing.
I then added all the spots on the dominoes together and made a total of 168.
It told me that Amy was missing 43 spots.
I was looking for four dominoes that totalled 43 spots.
I began with the highest domino (6:6) because we had to get a high number (43) with a low number of dominoes.
I worked out that the missing were 6:6, 5:6, 5:5 and 4:6. These four dominoes totalled the missing amount of 43 spots!

Amy needs to look after her dominoes by putting them in a safer place!

That's very true Bjorn.

Isobel from Ravensworth C.E. Primary School wrote:

In a full set there are 28 dominoes, therefore, there are 168 spots in a full set. In Amy's set there are four dominoes missing. These dominoes are 6/6, 6/5,6/4 and 5/5.

How about if there was one spot less missing - so that there were 126 spots. What might the possibilities be? Would there be more, fewer or could the problem not be solved?