Find two 10 digit numbers, each containing the digits from 0 to 9 once
and only once, with the property that successive pairs of digits, from
left to right, are divisible in turn by 2, 3, 4, 5, 6, 7, 8, 9, and
10.
(first pair is the first and second digit, second pair is the second
and third digit, third pair is the third and fourth digit etc...)

Hi aj9989,

Here you go:

1872549630

7812549630


I hope that helps. If you have any questions regarding my answer
please don't hesitate to ask before rating.

Best regards,
Rainbow

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Request for Answer Clarification by aj9989-ga on 17 Feb 2006 11:13 PST

Unfortunately, I dont see how this answers the question.

The question certainly leaves room for interpretation, but if you're
going to use multiplication or addition, I still don't see how it
works.

Take for instance the first number (1872549630).
1+8=9, 1*8=8   the multiplication is divisible by two
8+7=15,8*7=56  the addition is divisible by three but the multiplication is not

I could have misinterpreted the question, but can you justify your answer please?

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Clarification of Answer by rainbow-ga on 17 Feb 2006 17:12 PST

Take a look at the first answer as an example of how I interpreted the question:

1872549630

"first pair is the first and second digit, second pair is the second
and third digit, third pair is the third and fourth digit etc."

"successive pairs of digits, from left to right, are divisible in turn
by 2, 3, 4, 5, 6, 7, 8, 9, and 10."

first pair is 18 (first and second digit)
18 is divible by 2

second pair is 87 (second and third digit)
87 is divisible by 3

third pair is 72 (third and fourth digit)
72 is divisible by 4

fourth pair is 25 (fourth and fifth digit)
25 is divisible by 5

fifth pair is 54 (fifth and sixth digit)
54 is divisible by 6

sixth pair is 49 (sixth and seventh digit)
49 is divisible by 7

seventh pair is 96 (seventh and eighth digit)
96 is divisible by 8

eighth pair is 63 (eighth and ninth digit)
63 is divisible by 9

ninth pair is 30 (ninth and tenth digit)
30 is divisible by 10


Please let me know if you need further clarification.

Rainbow~

Excellent!  When I wasn't able to understand the answer as originally
stated (my own fault of understanding), rainbow was very accomodating!

Are you sure you are supposed to add the digits?
Maybe you are supposed to treat them as a new number...
18/2=9
87/3=29
72/4=18
25/5=5
54/6=9
49/7=7
96/8=12
63/9=7
90/10=9

Sorry, the last one is 30/10=3

I'm glad I could help. Thank you for the rating and tip.
Best regards,
Rainbow