Five singledigit positive integers appear in a sequence.
The sum of the first two is divisible by the second, but not by the first.
The sum of the first three is divisible by the third, but not by the first or the second.
The sum of the first four is divisible by the fourth, but not by the first, second or third.
The sum of the first five is divisible by the fifth, but not by the first, second, third or fourth.
What are the five integers, in order?
_____ _____ _____ _____
21
31
41
42 421
"" 423
51
61
62 621
63 631
71
81
82 821
"" 825
84 841
"" 842 8421
"" """ 8427
"" 843
"" 846 8461
"" """ 8463 84631
"" """ 8469
91
93 931
"" 932
"" 934 9341
The five digits in order such that the sum of the 1^{st} to the n^{th} digits are divisible by the n^{th} digit but not by any of the individual digits prior in the sequence is 84631.

Posted by Dej Mar
on 20111001 04:47:07 