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More Marbles

Age 11 to 14 Challenge Level:

This problem follows on from Marbles

Suppose I start with four marbles, one of each colour red, blue, green and yellow.

A red marble, blue marble, green marble and yellow marble

When I trade marbles I give away one marble of any colour and I receive one marble of each of the other three colours.

Can I trade marbles so that I will have exactly two marbles of each colour?

Can I have equal even numbers of each colour after a number of trades?

What about ending up with 5 marbles of each colour?

Is this possible and if so how many trades does it take?

Is it possible to end up with the same odd number of each colour for any odd number?