Save the gnomes from the terrible but fair Troll

    There are many puzzles about the poor gnomes, but I puffed on this one for the longest time, and even thought that I had proved that it was unsolvable - and it was solvable.

    So, the standard story: A

    cunning, but fair Troll caught a lot of gnomes (a lot - it means it is not known how many exactly, maybe a dozen, or maybe a lot more). He put them in a dark cave, where nothing is visible, and put on each gnome a hat, red or blue, in random order. And he said that tomorrow at dawn he would bring the gnomes one at a time and put them in a row in a row, so that the very last one would see all the nooks of the gnomes in front of him, the next one of all subsequent ones and so on, and the very first one would admire the dawn, but he would not see any of his brothers .
    Then, starting from the very last, the troll will ask each gnome what color the hat is on his head. Those who correctly guess the color of their hats will let go of the troll, and those who do not guess will eat the troll. Each gnome can only answer “blue” or “red”, nothing more can be said and done.

    Gnomes have time until the morning to come up with a strategy with the least losses, help the gnomes.

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