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You are standing next to an unlimited source of water (the tap in your kitchen). You need precisely 4.6 litres of water. Luckily you found two empty buckets. One can hold 4.3 and the other 4.7 litres of water. How can you measure the correct amount of water using the buckets when neither of them has graduation marks?

Problem #7 from: http://erityistehtavat.puolustusvoimat.fi/cyberchallenge.html

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  • $\begingroup$ Are you emptying the water into a container or must there just be collectively 4.6 liters in the buckets? $\endgroup$ – MoldovanHipster Jul 17 '15 at 19:34
  • $\begingroup$ I believe there will be collectively be 4.6 liters in the buckets. But the question did not specify. $\endgroup$ – bigC5012 Jul 17 '15 at 19:39
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    $\begingroup$ You mean you didn't write this question yourself? If it's not your own, you should credit the source. $\endgroup$ – dennisdeems Jul 17 '15 at 19:42
  • $\begingroup$ Similar to problem in the movie die hard $\endgroup$ – Maxqueue Jul 17 '15 at 19:43
  • $\begingroup$ As this question seems to be from an ongoing competition, it has been locked and its answers have been temporarily deleted. They will be reinstated on or around July 21st when the competition is over. $\endgroup$ – Aza Jul 17 '15 at 20:51
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If we fill up the bucket holding 4.7L and fill the 4.3L with it, then we will have .4L left inside the 4.7L bucket. Dump the water in the 4.3L bucket, and pour the .4L into it. Now fill up the 4.7L bucket again, and fill the smaller bucket once again. Since it already contined .4L, the larger bucket will be left with .8L. Dump the small bucket and pour the .8L of water into the small bucket. Repeat these steps, each iteration adding .4L more to the "running total."

We keep on doing this until the small bucket contains 4L. Now filling it to the brim with the big bucket will leave 4.4L of water inside the big bucket. Dump the small bucket once again and fill it with the 4.4L of the big bucket, leaving only .1L inside the big bucket. Dump the small bucket again and put place the .1L of water inside the small bucket.

So we repeat what we did before, each time adding .4L to the running total: .1L, .5L, ..., 4.1L. With 4.1L in the small bucket, we fill up the big bucket and top off the small bucket and get left with 4.5L in the big bucket. Dumping out the water inside the small bucket and filling it up again with the big bucket, we get left with .2L in the big bucket. We dump the small bucket, and put the .2L inside the small bucket.

One more time! We continue the same set of operations as before, effectively adding .4L to the running total each time: .2L, .6L, ..., 4.2L. Once we hit 4.2L. We fill up the big bucket and use it to fill the smaller bucket. This takes only .1L, so we get left with 4.6L inside the big bucket.

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