Puzzles Question:
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Substitute digits for the letters to make the following Division true

O U T
-------------
S T E M | D E M I S E

| D M O C
-------------
T U I S

S T E M
----------
Z Z Z E

Z U M M
--------
I S T

Note that the leftmost letter cant be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be 3?

Answer:

C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9

It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).
S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T) must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).

Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.

O U T 4 1 3
------------- -------------
S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8

| D M O C | 9 5 4 0
------------- -------------
T U I S 3 1 6 2

S T E M 2 3 8 5
---------- ----------
Z Z Z E 7 7 7 8

Z U M M 7 1 5 5
-------- --------
I S T 6 2 3

Also, when arranged from 0 to 9, it spells CUSTOMIZED.

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There are 10 statements written on a piece of paper:

1. At least one of statements 9 and 10 is true.
2. This either is the first true or the first false statement.
3. There are three consecutive statements, which are false.
4. The difference between the numbers of the last true and the first true statement divides the number, that is to be found.
5. The sum of the numbers of the true statements is the number, that is to be found.
6. This is not the last true statement.
7. The number of each true statement divides the number, that is to be found.
8. The number that is to be found is the percentage of true statements.
9. The number of divisors of the number, that is to be found, (apart from 1 and itself) is greater than the sum of the numbers of the true statements.
10. There are no three consecutive true statements.

Find the minimal possible number?
What are the next three numbers in the given series?

1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 ?