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Camy made a list of every possible distinct five-digit positive integer that can be formed using each of the digits 1, 3, 4, 5 and 6 exactly once in each integer. What is the sum of the integers on Camy's list?

 Sep 29, 2021
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1, 3, 4, 5, 6 =5! ==120 permutations as follows:

 

(13456, 13465, 13546, 13564, 13645, 13654, 14356, 14365, 14536, 14563, 14635, 14653, 15346, 15364, 15436, 15463, 15634, 15643, 16345, 16354, 16435, 16453, 16534, 16543, 31456, 31465, 31546, 31564, 31645, 31654, 34156, 34165, 34516, 34561, 34615, 34651, 35146, 35164, 35416, 35461, 35614, 35641, 36145, 36154, 36415, 36451, 36514, 36541, 41356, 41365, 41536, 41563, 41635, 41653, 43156, 43165, 43516, 43561, 43615, 43651, 45136, 45163, 45316, 45361, 45613, 45631, 46135, 46153, 46315, 46351, 46513, 46531, 51346, 51364, 51436, 51463, 51634, 51643, 53146, 53164, 53416, 53461, 53614, 53641, 54136, 54163, 54316, 54361, 54613, 54631, 56134, 56143, 56314, 56341, 56413, 56431, 61345, 61354, 61435, 61453, 61534, 61543, 63145, 63154, 63415, 63451, 63514, 63541, 64135, 64153, 64315, 64351, 64513, 64531, 65134, 65143, 65314, 65341, 65413, 65431)

Total Sum ==5,066,616

 Sep 30, 2021

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