- #1

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Reading from left to right, if you take the first digit of the above number it may be divided by one.

If you take the first two digits, '12' this number is divisible by two.

If you take the first three digits '123' this number is divisible by three.

However if you take the first four digits '1234' this number is not divisible by four.

If we transpose the 4 and 6 and make the number 1236547890 we may proceed.

We can now take the first four digits '1236' and this number may be divided by 4 and the first five digits 12365 may be divided by 5 and the first six digits 123654 divided by 6.

Unfortunately 1236547 cannot be divided by 7 nor can we change the 7 for a 3 as it has already been used and the digits 8, 9, 0, will not fit.

This particular series of numbers does not satisfy the divisional requirement.

The question is-

What would be the order of the digits which would satisfy the divisional requirement already shown and also allow the divisional progression to proceed for the remaining part of the 10 digit number.

Pocket calculators and slide-rules may be used.