What if he'd hoped for 18000 spears? The total number of spears hoped for isnt stated, therefore we cannot assume that 6001 is exactly half of the total.
In this instance we can tell it's 6001 though.
therefore we cannot assume that 6001 is exactly half of the total.
Correct, all we can deduce is the bounds:
Let x be the number of spears hoped for.
6000 < x/2 < 6002
12000 < x < 12004
Edit: fixed error
Why would you need to assume? If 6000<50% AND 6002>50%, he wishes for 12002 spears.
Edit: dammit, that's a lot of spears.
Because the number you're reasoning about is the number of spears he wished for, not half the number he wished for, so mathematically, the logic holds for 3 different possible wished for integer values.
To arrive at precisely 12002 you need to make a further assumption which nobody has explained so far.
Also, a minor point, but that he wished for an integer number of spears is another assumption. Albeit a very reasonable seeming one, it's an assumption none the less. He could have wished for 12 thousand and π spears, for example. And no, I have no idea what you'd do with that ~14% of a spear.
If this were an SAT question, and upvotes correlated to what people were answering, well, the majority got this question wrong.
He had hoped for precisely 12002 spears.
Or 12003
Or 12001
