12. (5 points) Initially, there are three cards in the box, each with the numbers $1, 2, 3$ written on them. Each time, two cards are taken out of the box, the sum of the numbers on them is written on another blank card, and one card is put back into the box. After 5 such operations, except for the last card with the written number, all other cards have been taken out at least once and no more than twice. What is the largest number on the card in the box at this point?
【Analysis】From the given information: In the end, a total of 8 numbers are obtained, and all the numbers are added $2 \times 5=10$ times in total. Since each card is taken at least once and no more than twice, 4 numbers are calculated once, and the seventh number is only calculated once by the eighth number. Therefore, the seventh number is only calculated once. To make the number on the card as large as possible, the 4th, 5th, and 6th numbers should be calculated twice, and the 1st, 2nd, and 3rd numbers should be calculated once. This can make the 8th number the largest. The problem can be solved by discussing different cases.

【Solution】From the analysis, we can conclude:
To make the number on the card as large as possible,
the 4th, 5th, and 6th numbers should be calculated twice, and the 1st, 2nd, and 3rd numbers should be calculated once.
This can make the 8th number the largest.
(1) $1,2,3,4,6,10,16,26$
(2) $1,2,3,3,6,9,15,24$
(3) $1,2,3,5,6,11,17,28$
Answer: The largest number on the card in the box is 28.