A farmer hired a guy to deliver tomatoes to his neighbors, the first neighbor got 1/2 the tomatoes plus 1/2 a tomato, the 2nd neighbor got half the remaining tomatoes plus a 1/2, the third neighbor got half the remaining plus a 1/2. The delivery guy was to keep one tomato...how many did he start with?
Posted by Rita at March 6, 2006 08:12 AMThe answer (in Pig Latin, so as not to spoil it for others) is entytway ivefay. But I cheated a bit by using Mathematica to solve the set of linear equations representing the problem.
Posted by: stepan at March 6, 2006 11:51 AMYou have GOT to be kidding! But, if not, I'll go with Stepan and say "25."
Posted by: Leah at March 6, 2006 02:16 PMMathematica must be a bit flawed, because I believe the correct answer is 15.
Posted by: me at March 6, 2006 05:03 PMFirst of all, this - with the possible substitution of apples for tomatoes - was the puzzler on this weeks's Car Talk show on NPR. I first solved it using brute force, but below is the method described on the show.
Let x be the number of apples left at the last stop. Then what do we know?
x - (x/2 + 1/2) = 1
where the number in parentheses is the number of tomatoes given to the 3rd neighbor. Multiply both sides by 2:
2x - x - 1 = 2
So x = 3
Let y be the number of apples at the 2nd stop. What do we know?
y - (y/2 + 1/2) = 3
Multiply both sides by 2:
2y - y - 1 = 6
so y = 7
Let z be the number of apples at the 1st stop. Note that z is the number we are looking for. What do we know?
z - (z/2 + 1/2) = 7
So 2z - z - 1 = 14
So z = 15
Posted by: Pat at March 7, 2006 10:28 PMHmmm. I am eagerly awaiting Stepan's next comment.
Posted by: Elizabeth (niece) at March 8, 2006 12:20 AMAre you saying that entytway ivefay is NOT pig latin for "15"? I must have been confused by all those other languages...
But y'all are correct in that Leah's answer is wrong! :-P
It turns out my set of linear equations was incorrect. The correct ones (which you can test here) should have been:
System: {f1=0.5x+0.5,r1=x-f1,f2=0.5r1+0.5,r2=r1-f2,f3=0.5r2+0.5,1=r2-f3}Posted by: stepan at March 8, 2006 09:10 AM
Unknowns: {x,f1,f2,f3,r1,r2}
epansta aswa ongwra...
Posted by: me at March 8, 2006 09:39 PMApparently so! I'm just curious to know where he diverged from the truth. I'm not knocking his effort, don't get me wrong. He did more than me; I feel happy these days to set the dishwasher on the right cycle.
Posted by: Elizabeth (niece) at March 9, 2006 12:24 AM