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July 4th, 2018, 11:55 PM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  [ASK] Exact Measure Using Two Bottles
Someone wants to take 4 liters of water, but he only has two 5liters and 3liters bottles. How is he able to measure 4 liters with only those bottles?

July 5th, 2018, 08:14 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,780 Thanks: 970 
3 : 5  0 : 0 3 : 0 0 : 3 3 : 3 1 : 5 1 : 0 0 : 1 3 : 1 0 : 4 
July 5th, 2018, 06:43 PM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 
Thanks, Denis McField!

July 5th, 2018, 06:47 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,780 Thanks: 970 
Bienvenu, Monsieur LaMouche!

July 10th, 2018, 01:31 PM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 
The phrasing "two 5liters and 3liters bottles" is ambiguous. I first read it as "two 5liter bottles and a 3liter bottle". But only one 5liter bottle is needed. The original post should have said "two bottles, one 5liters and the other 3liters" or just "a 5 liter bottle and a 3liter bottle".

July 10th, 2018, 01:37 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,780 Thanks: 970 
You have 2 bottles. One contains 5 liters, the other contains 3 liters. 
July 10th, 2018, 01:58 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
3 : 5  0 : 0 0 : 5 3 : 2 0 : 2 2 : 0 2 : 5 3 : 4 0 : 4 (if required) or just halffill each bottle. 
July 10th, 2018, 02:51 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,780 Thanks: 970  
July 10th, 2018, 10:55 PM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
How does one fill it, then, without halffilling it first?

July 11th, 2018, 05:38 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,780 Thanks: 970 
Ahhhhh....that's why they pay you the big bucks!!!!!!!!!!!!! Idea: fill container, then tilt it such that the water level line from bottom side to opposite top side is a straight line... like a rectangle's diagonal...leaves exactly 1/2 contents Then 2 moves only: 1: fill C5, tilt: 2.5 left 2: fill C3, tilt while holding directly above C5; the escaping 1.5 will fall in C5, so C5 ends up with 4 Impressed????? 

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bottles, exact, measure 
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