## The number 1234512345123451234512345

The largest remaining number is **553451234512345**. To see this, we can assume that the cuts are made from left to right. If we stop cutting all four digits, the remaining number will start with 1, 2, 3, or 4. Therefore, less than the number above. This done, if we stop cutting the second sequence 1234, the remaining number will have in the first or second fret, left to right, 1, 2, 3, or 4. Even smaller than the number above. The first two 5 should remain, because if one of them is removed, we complete 9 withdrawals and then some digit of the third sequence 1234 will appear in 1^{The} or at 2^{The} home. Finally we must cut sequence 12, which occupies 11^{The} and 12^{The} position.

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