Anybody have a suggestion what I can do with 10 flavorless fresh apricots?

They got eaten up? So I'm too late with my suggestion?? Oh, man.....

Puree and freeze. I think it'll be good for applesauce substitute when making cake, especially that it has really mild flavor.

Thanks to everybody for the great answers! Here's what happened: This morning we babysat for our three grandchildren and unnoticed by me, the three of them ate all the apricots (which were sitting on the counter awaiting their fate). So problem solved, although I now wish I had had the opportunity to try some of the intriguing solutions offered here. Now I want those tasteless apricots back!

Stuff with finely diced preserved lemon, drizzle with honey and bake until soft serve with roast chicken and with a dollop of Greek yoghurt or panned

Apricot facial?

Yes, but you can't go around saying stuff like that to people. Just kidding, ha ha- you could cook them down in some orange juice and end up with something surprisingly like stewed prunes, if that appeals.

Apricot Upside Down Cake.

You could pickle them. Unless the flesh is mealy, the texture should still be amazing even if the taste isn't very apricot-y. Definitely use some star anise and cinnamon in the pickling liquid to amp some warming flavors.

http://www.myfriendmaillard.com

You could stew them in some more flavorful apricot nectar (bottled/canned) with a little honey or sugar, and a squeeze of lemon. Then puree the cooked mixture and use it as a sauce/coulis on ice cream, panna cotta, or custard...or in cocktails - Bellinis, etc.

Peel and puree, then use in place of part of the oil in a recipe you are baking (like banana bread).

Personally, I think I'd blanche them to remove the skins, then pit. The resultant apricot "meat" I'd freeze and eventually cook with another batch of more flavorful apricots.

Roasting them—with vanilla bean and raw sugar (like here: https://food52.com/recipes/23703-roasted-plums-with-vanilla-bean)—might coax out some of the flavor. You could also make a shrub: https://food52.com/blog/13831-how-to-make-shrubs-aka-drinking-vinegars-without-a-recipe. If they're not flavorful enough on their own, you could combine them with another, tastier fruit! Like pineapple. Or mango!