two teasers about ten-digit numbers

radosr

Baruch MFE Faculty
A 10-digit number A will be written as a_1a_2a_3...a_10. Two separate questions:

1. Suppose a_1 is the number of times the digit '0' appears in A; a_2 is the number of times '1' appears in A, and so on... a_10 is the number of times '9' appears. What is A?

2. (more difficult) A contains each of the digits from 0 to 9 exactly once. The number a_1 is divisible by one. The number a_1a_2 is divisible by two. The number a_1a_2a_3 is divisible by three, and so on...What is A?
 
A 10-digit number A will be written as a_1a_2a_3...a_10. Two separate questions:

2. (more difficult) lol A contains each of the digits from 0 to 9 exactly once. The number a_1 is divisible by one. The number a_1a_2 is divisible by two. The number a_1a_2a_3 is divisible by three, and so on...What is A?

1234567890. Why scratch a head (if I got the problem correctly) or you should have baned this response.
 
3816547290

firs you figure 0, then 5. then 6-4 combo, then 2, then 8. these are forced. two possibilities for a7: 3 or 7, each of which gives 4 or 6 numbers to check.
 
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