Numbers like 12345, 13542 and 21435 are some of the 120 different arrangements that can be made from the digits 1, 2 , 3, 4 and 5. If all 120 arrangements are placed in ascending manner, what will be the 87th number?
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The hundredths place would change after the tenths and ones would interchange twice. 12345, 12354 would be followed by 12435. See that 4 changes from 3 after the ones and tenths change twice. The thousandths would then be replaced after 6 times the hundredths, tenths and ones would change. or simply 3 x 2 = 6. the ten thousandths place would change after 4 x 3 x 2 = 24 times due to the permutation followed. now 87 divided by 24 would leave 3 remainder 15. That means from 1-24 you will have 1 in your ten thousandths place, 2 from 25-48, and 3 from 49-72, so from 73 to 96, you will use 4 in your ten thousandths place, with 1,2,3 and 5 as your remaining numbers. Obviously in your 73rd number, you will have your thousandths spot be occupied by 1, your hundredths by 2, tenths by 3, and ones by 5, giving 41235 as your 73rd term. following the the pattern of interchanging, 2 will occupy the thousandths place at the 79th term, and 3 will occupy the thousandths at the 85th term, which by logic the smallest number would be 43125, by the 86th would be 43152 and the 87th 43215. There you go PAPA P. Love Aldrin, Bague, Paolo, Jared, Jerome, Medina, Joshua, Mondy, Quilit, Bryan, Divine Grace, Angelo and the whole UST REE BATCH Sept. 2014. hindi totoong pangalan to account na to <3.