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Amy's Dominoes

Age 7 to 11 Challenge Level:
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.

Early in 2015 we had a solution from Suzanne and another. I've summarised the method they used. It shows are rather different way of journeying through the challenge. Showing how to work out how many dots there are in a set of dominoes.

They noticed that the number that you are looking at is always 2 more than that number you are considering. Two more because there’s one of them with a zero and another that goes to make the double domino. They called the number that you are considering n and the number that there are of them they called a and a is always 2 more than n.. They also realized that you had to add the numbers below n.
As an example when n = 5 the number of dots on all the fives is n x a, i.e. 5 x 7, plus 1 + 2 + 3 + 4. S there’s 35 + 10, i.e. 45 dots on all the 5’s.

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?
Well a very good explanation of the first challenge and this further one came from Woodcote School in Oxfordshire. You can see it here.    
P.doc P.pdf