Hard problem with fractionsI can't solve the following problem.A person is x years old. Find his age if the following is true. In a group of x people each one started taking pictures of each of the others. At some point we know that more than 1 2 of the people has taken exactly 1 2 of all of their pictures (which are x − 1 for every one of them), at the same time more than 1 3 of them has taken exactly 1 3 of all of their pictures, and at the same time more than 1 7 of them has taken exactly 1 7 of their pictures.

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Hard problem with fractionsI can&#039;t solve the following problem.A person is x years old. Find his age if the following is true. In a group of x people each one started taking pictures of each of the others. At some point we know that more than       1    2   of the people has taken exactly       1    2   of all of their pictures (which are   x  −  1 for every one of them), at the same time more than       1    3   of them has taken exactly       1    3   of all of their pictures, and at the same time more than       1    7   of them has taken exactly       1    7   of their pictures.

hildiadau0o · Accepted Answer

From the pictures taken we know 2, 3 and 7 are all divisors of   x  −  1. The smallest number for which this true is 2*3*7 = 42. Hence the smallest x is 43. The next possible x would be 2 * 42 + 1 = 85. Now        1    2   of 42 is 21,       1    3   of 42 is 14 and       1    7   of 42 is 6. Since more than half,a third, a seventh of the people have taken their pictures, the minimum number of people would be   (  21  +  1  )  +  (  14  +  1  )  +  (  6  +  1  )  =  45 which excludes 43 as a solution.In case of    x  =  85 we get   (  42  +  1  )  +  (  28  +  1  )  +  (  12  +  1  )  =  85 , which suits perfectly.I guess we can safely assume the person isn&#039;t 127 years old.

Hard problem with fractions I can't solve the following problem. A person is x years old. Find his

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