# Find this number anyway

**Logic**Level pending

Consider a 10-digit number \(M = \overline{ABCDEFGHIJ}\) made from different single digits.

You are given the following information about \(M\)

- \(B = I - 4\) or \(B = E + 4\) anyway
- \(A = \dfrac B3\) or \(A = G + 3\) anyway
- \(C = J + 2\) or \(C = 3 \cdot F\) anyway
- \(D = 4 \cdot G\) or \(D = \dfrac E3\) anyway
- \(E = J - 1\) or \(E = \dfrac D4\) anyway
- \(F = 2 \cdot B\) or \(F = A - 4\) anyway
- \(G = F + 1\) or \(G = I - 3\) anyway
- \(H = \dfrac A2\) or \(H = 3 \cdot C\) anyway
- \(I = H + 3\) or \(I = \dfrac D2\) anyway
- \(J = H - 2\) or \(J = 2 \cdot C\) anyway

Knowing that or is here "exclusive disjunction" meaning either one or the other but not both or the XOR operator, find the number anyway.

Of course you should insert your answer as \(M + 101000001\) just for the fun of the question being proposed anyway.