OK so there is this black velvet bag that contains a bunch of uniquely numbered
Every puzzle has numbered balls. Enough with the balls. This puzzle has spoons.
You will be asked two questions about these spoons.
In order to get the needed information I ask my beautiful assistant here [pic load failed; sorry ]
to remove from the bag some quantity of spoons, add their numbers and write it on a sheet of paper.
She looks at you, smiles, and suggests that should be enough information for you.
You disagree and ask her to replace the spoons and repeat the process, which she does,
drawing the same number of spoons from the bag but this time the sum she writes is a different number.
You ask her to do it again. And again, ... until the sums begin to repeat themselves, and eventually
you are convinced that no more new numbers will appear.
She then erases any duplicates, keeping only one occurrence of each, and hands you the paper.
On it you see:
115 118 113 110 120 117 116 112 121 114
Then you are asked:
How many spoons are in the bag, and what are their numbers?
You think for only a moment and say that you need more information,
like how many spoons were drawn each time.
My smiling assistant says she can't tell you that; but she can tell you that the sum of the number
of spoons in the bag and the number of spoons drawn each time is an odd number.
You pull out a used envelope, turn it over [everyone does this], scribble something,
and then give your answer.