This is a problem I often see in exams, it involves calculating the least number of weighing operations needed to get the weight asked.
It states this:
Allison has a bag of rice which weighs more than 17 ounces and she has a two pan balance and 4 different weights being 3 oz, 4 oz, 7 oz and 11 oz respectively. How many times at least does she has to use the balance to get 17oz of rice?
I tried to solve this problem by summing up all the weighs:
Since what it is being asked is to get $17$ ounces what I tried to do is to find the possible combinations which put in each pan so that they sum up to 17.
But grouping either $11$ in one side and $3+4+7$ in the other the resulting weight is $3$. If I choose not to use one of the weights let's say $11$ and $4+7$ it cancels both sides, while $3+7$ produces $1$ ounce in the other side therefore it cannot be used, if it is $3+4$ it produces $4$ ounces. So it seems it is impossible to get the $17$ ounces at once.
The other choice would be just using in the first attempt just $3$ and $7$, and in the second turn just the weight of $7$ ounce. Therefore the least number of times to use the balance would be $2$. But this answer is not correct.
The method I tried to use I don't think it is right, it is prone to errors and more importantly is tedious which is something I can't use at an exam where time is limited.
Can somebody help me to find a more orderly and logical method step by step to solve these kind of problems other than just guessing and starting to plug in numbers randomly as if I was trying to hit a target?.