Let's imagine we have two boxes of numbered cards, and the first box contains the cards numbered 2 to 8, and the second box contains 0, 1 and 9.

Starting with the cards in the first box we start to place the cards in order:

2, 3, 4, 5, 6, 7, 8 is the order because we don't have 1 or 9. Call this set 1.

Then we take two cards to form a number from the second box:

So we could have (not in order) 00, 01, 09, 10, 11, 19, 90, 91, 99.

First, remove leading zeroes: 0, 1, 9, 10, 11, 19, 90, 91, 99.

Then remove anything less than any of the numbers in set 1: 9, 10, 11, 19, 90, 91, 99. There are 7 numbers in this set, and 7 numbers in set 1.

The first 4 of these correspond to the given numbers, but in a different order: 11, 9, 19, 10.

 1 9 0 0 01 09 00 1 11 19 10 9 91 99 90

All the combinations of 0, 1 and 9 are shown in the table above, and 00 have been deleted, leaving, in order, 9, 11, 19, 10, 91, 99, 90. So 91, 99, 90 complete the series according to this logic.

by Top Rated User (1.1m points)