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Baby is two years old now and drinks milk by the quarter pint, so we have decided to call her GILL. Getting her to recognise her name proved difficult, so we put the letters G, I, L, L on separate building blocks. She loves arranging them, but rarely gets them in the right order. One day she managed to produce every possible four-letter 'word': LILG is one such. How many different four-letter words did she produce that day?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.