Independently of each other, two people think of a number between 1 and 10. What is the probability that five or more numbers will separate thetwo numbers chosen at random by the two people?
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Here is a suggestion. Draw a 10x10 grid. There will be 100 lattice points, pairs of integers, (1,1) to (10,10). Count the number pf pairs that works. For example, the pairs (4,9) & (9,4) both work. How many others are there?
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