## Task 4 - 310514

Thomas writes the number 2375246895 on the board and explains that it was created by writing three numbers in sequence. These three numbers were written in ascending order, starting with the smallest. None of the three numbers contains a digit more than once.

a) Sebastian suspects that the three numbers are 2, 375, and 246895; because they match Thomas's description.

Werner counters: "The description by Thomas can also be satisfied by three other numbers." Is this correct? Justify your answer!

b) Change one digit in the number written by Thomas so that there is then only one way to satisfy the description with three numbers. Name (for the change you have chosen) this one possibility for the three numbers!

A justification is not required.
a) The specifications can also be met by three other numbers. For justification, it suffices to mention two of the following possibilities (a hint for 2, 375, 246895 is sufficient):

$$
\begin{gathered}
2,3,75246895 ; \quad 2,37,5246895 ; \quad 2,375,246895 ; \quad 2,3752,46895 \\
23,75,246895 ; \quad 23,752,46895 ; \quad 237,524,6895
\end{gathered}
$$

b) If, for example, the digit 4 is changed to 6, choosing 2375266895 as the number to be written, then there is only the possibility that 237, 526, 6895 are the three numbers.

Solutions of the 1st Round 1991 adopted from [5]

### 2.32.2 2nd Round 1991, Class 5