If I remember correctly, only some of the diamonds will be present depending on which area you start in at the beginning of the game. You start at one of four locations depending on which character you choose, and a diamond case will spawn there as part of the tutorial. The diamond cases that would normally present as part of the tutorial in the other locations will not spawn, so it is highly likely that those three are the cases you are talking about. So you shouldn't need to restart the game; those cases won't be there in your save file.
More info here:
https://farcry2.fandom.com/wiki/Diamond_Cases#The_1st_Diamon...