The logic is the following.
The worst case scenario is that you draw the first 13 cards of the same colour, then another 13 of the same color then another 13 of the same color. After 39 cards, you draw all 3 colors. Then to ensure that you have at least 3 of each, you need to take another 3 cards of the 4th left colour. So in total after 42 card you can be sure you have at least 3 cards of each color (since we considered here the worst case scenario).

By the same logic, if you are asked how many cards you have to draw to ensure you have three of the same colour (not 3 of EACH), the answer is 9.
Here the worst case scenario is that you draw first 4 cards of different colour, then another 4 of different color. After 8 cards, you have two of each colour. So when you draw the 9th card, you are sure you have at least 3 cards of the same colour.
Hope this helps.

42 is right... but I do not get it.

Help me with the logic!

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