Brain Teasers
Divisorama
Arrange the numerals "123456789" to form a 9-digit number (referred to as "ABCDEFGHI") whose 2-digit subsets meet the following criteria:
1) AB is divisible by 2
2) BC is divisible by 3
3) CD is divisible by 4
4) DE is divisible by 5
5) EF is divisible by 6
6) FG is divisible by 7
7) GH is divisible by 8
8) HI is divisible by 9
There are two solutions.
1) AB is divisible by 2
2) BC is divisible by 3
3) CD is divisible by 4
4) DE is divisible by 5
5) EF is divisible by 6
6) FG is divisible by 7
7) GH is divisible by 8
8) HI is divisible by 9
There are two solutions.
Answer
781254963 and 187254963AB, CD, EF, and GH must be divisible by even divisors. Therefore B, D, F, and H must be even numerals. This means that A, C, E, G, and I are odd numerals. DE must be divisible by 5, therefore E is 5. EF must be divisible by 6, therefore EF is 54. FG must be divisible by 7, therefore FG is 49. GH must be divisible by 8, therefore GH is 96. GH must be divisible by 9, therefore GH is 63. The last five digits have now been determined to be 54963. To be divisible by 4, CD must end in 2. This makes B equal 8. The digits are now ?8?254963. The remaining digits, 1 and 7, can be placed into either remaining location.
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