you have two cups with capacity 17 and 5 ounces....

Question

you have two cups with capacity 17 and 5 ounces. There are no markings on the cups, and you are not able to mark the cups in any way. You are given a huge bucket of water. Is it possible to measure and place exactly 13 ounces of water into the big cup? If so, carefully explain your method; if not, carefully explain why not

Answer 1

In math terms, this is:
   13 = 6(5) - 1(17)
   13 = (5+5+5+5+5+5) - 17
   13 = (5+5+5+(2+3)+5+5) - 17
   13 = (5+5+5+2) + (3 + 5 + 5) - 17
   13 = (5+5+5+2) -17 + (3 + 5 + 5)

   13 = ( (5+5+5+2) - 17) + (3) + 5 + 5

   13 = 0 + 3 + 5 + 5

Fill 5-oz container 4 times and pour into 17-oz container each time. This leaves 3 oz in the 5-oz container. Dump the now-full 17-oz container. Pour the 3 oz from the 5-oz container into the 17-oz container, then fill the 5-oz container two more times and pour into the 17-oz container.

NOTE: Find the math equivalent, then translate to word procedure -- no grouping of parenthesis may exceed container capacity.  "+" is fill; "-" is pour or dump.

Answer 2

Hi Danielle, the answer to your question is yes, it is possible to place exactly 13 ounces of water into the big cup.

 

Start by filling the 5 ounce cup and dumping it into the 17 ounce cup. Repeat this process two more times.

 

The 17 ounce cup now has 15 ounces of water in it.

 

Fill the 5 ounce cup one more time. With the 5 ounce cup, fill the 17 ounce cup to the top. 2 ounces of water will fill the 17 ounce cup to the top. This will leave 3 ounces of water in the 5 ounce cup.

 

Now, empty completely the 17 ounce cup.

 

Dump the remaining 3 ounces of water in the 5 ounce cup into the 17 ounce cup.

 

Fill the 5 ounce cup again and dump it into the 17 ounce cup. Repeat the process one more time. 

 

The 17 ounce cup now has the required 13 ounces of water.

 

Questions?