Wednesday, 2 March 2011

Token solution and commentary

In my last post I offered this little number problem, for which I now provide a solution.

Two children, Mike and Nina, are collecting tokens for a free gift from a store. They both have some tokens, but Mike needs 49 more and Nina needs 2 more to get the gift. They decide to put their tokens together, but they still do not have enough to get the gift. How many tokens did they each have?

What is needed here is to focus on N. She needs only two more tokens. If M gives her all his tokens she still does not have enough to get the gift. Because she needs only two more then this means that M must have only one token! From this you can easily deduce that the gift requires 50 tokens and so Nina has 48.

I am intrigued at how difficult this problem seems to be for some individuals! Children can't resist the temptation to add the 49 and the 2, and then don't know what to do with the answer.

I had some interesting responses to this post. Christina solved it immediately (clever wife). Jack did it with a little nudge from Grandad. Someone else wrote: 'I seem to know the answer however I'm not entirely sure how I got to it!' Brenda and Ron wrote: 'We can't get our heads around this problem! Is there some missing information, or are we just thick?'

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