[Decimal numeral system] Riddles $\quad]$

Top student Polikarp and underachiever Kolya were forming the smallest 5-digit number consisting of different even digits. Polikarp formed his number correctly, while Kolya made a mistake. However, it turned out that the difference between Kolya's number and the correct answer is less than 100. What numbers did Polikarp and Kolya form?
Think about what the first two digits of Polycarp's number and the last two digits of Kolya's number should be.

## Solution

If we proceed as in the previous problem, Polycarp should have formed the number 02468, but the first digit cannot be zero, so Polycarp formed the number 20468. Let's try to find Kolya's number. It is greater than Polycarp's number but consists of the same digits. The first three digits cannot be changed, as this would make the difference between Kolya's and Polycarp's numbers greater than 100. Only the fourth digit can be changed, and it can only be swapped with the fifth digit, otherwise the difference would again be greater than 100. Therefore, Kolya's number is 20486.

## Answer

20486.