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The man tells you, "To enter the door of infinite precision, you must complete all of these tasks perfectly:

  • Hold in front of me a baby that is exactly two days old.
  • Bring me a metal object that weighs exactly one kilogram.*
  • Bring me a stone object that weighs exactly one pound.*
  • Bring me a glass containing something other than water that is exactly the same density as water.
  • Write all the digits of pi."

"I'm sorry", you say, "but that is impossible. I can complete four, but there is one I cannot do."

Which task can't you accomplish, and why?

(The explanation should state how you can do the other four tasks, as well).

Hint:

Keep in mind that this puzzle was spoken, not written down. This may help with one of the tasks.

*If you want to get technical (and I know some of you do), consider these objects with a mass of one kilogram and one pound.

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    $\begingroup$ Love when the answer seems so obvious you're scared to answer! Ha! $\endgroup$ – Brent Hackers Jun 7 '16 at 7:23
  • $\begingroup$ Have you actually been given "this piece of paper" ? $\endgroup$ – BmyGuest Jun 7 '16 at 7:36
  • $\begingroup$ Do you have a pen that will write on "this piece of paper"? $\endgroup$ – Brent Hackers Jun 7 '16 at 8:00
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    $\begingroup$ So...what's the precise moment of birth, crowning? Placental afterbirth? First breath? Cutting the umbilical cord? An arbitrary timestamp taken by a bystander? What if its a c-section? If it's not on the birth certificate, is it not "certified"? $\endgroup$ – user662852 Jun 7 '16 at 11:29
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    $\begingroup$ This question has been reworded five times so far (currently at revision 6). I guess OP is not ready to enter the door of infinite precision any time soon (more precisely, in fintie time). $\endgroup$ – Marc van Leeuwen Jun 8 '16 at 5:40
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The task you can't accomplish is:

Bring an object with a weight of exactly one pound. Nothing is exactly one pound with infinite precision. There are several definitions of the pound, but the most common one is defined as "0.45359237 kilograms". No matter how hard you try, you aren't going to make something with that exact weight, it will weigh slightly more or slightly less. There are several other definitions of the pound, but they all have the same problem. At least one of them is defined by an "official object" but it is not made of stone. As some people have pointed out, there are solutions for "weight" in the precise sense of that word. I was really thinking of mass but was imprecise (as this distinction is not present in common language). If you want to take it as "weight" then fair enough, in that case all tasks are possible.

How you can accomplish the other tasks:

If you hold a baby that is slightly less than two days old, until it is slightly more than two days old, it will pass through the exact moment of being two days old.

...

A kilogram is defined as "equal to the mass of the International Prototype of the Kilogram" (which is metal). So you can bring this object, which is exactly one kilogram by definition. (This would be difficult, as you would have to steal it or convince someone to let you borrow it...but it's not logically impossible).

...

You couldn't make anything of an exact specified density. However, since the temperature and pressure of the water are not specified, you only have to get within the range of potential densities of water, which is an easy task.

...

I had in mind that you write the phrase "all the digits of pi" on a piece of paper. Given that this is a spoken puzzle, it surely fulfills one interpretation of what the man said. However, I suppose you could write 0123456789, as an alternative suggested by Brent Hackers.

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    $\begingroup$ I don't believe this answer is accurate. A pound may have several definitions, but at one point in space, there is a pound. I would bring the questioner a pound+ of something, and let the extra evaporate slowly. Like the baby passing through the two year mark, the item will eventually weigh a pound per the kilogram definition. How long will it weigh the correct amount? Probably longer than the baby was exactly 2 years old... $\endgroup$ – Tony Ennis Jun 7 '16 at 13:15
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    $\begingroup$ @CemKalyoncu it is rational. But the odds that a particular set of molecules add up to exactly 0.45359237 of the set of molecules in the official Kilogram seem very small. And even if there were such a possibility, there is no way you could measure the official kilogram or construct the stone with sufficient precision. $\endgroup$ – user21939 Jun 7 '16 at 13:55
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    $\begingroup$ Just move the stone up and down, and its weight will change with the gravity changes. $\endgroup$ – Tony Ennis Jun 7 '16 at 14:09
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    $\begingroup$ @dan1111 "the odds are very small" is far from a proof. "Stone" is very undefined, so you can toy with a lot of different elements and their isotopes. Considering that 1kg 'metal' is composed of an integer vale of neutrons, protons and electrons, I'm rather positive you can get to the same integer values building a stone when using trace elements to balance out the numbers. Now HOW one would practically build a 'stone' at atomic precision is another question, but hard != impossible. $\endgroup$ – BmyGuest Jun 7 '16 at 17:57
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    $\begingroup$ This has gotten very technical. Far beyond the intent of the puzzle? Interesting as the discussion is, I can't help but think that the spirit of the puzzle is a little broken. Also, I think the knowledge and science tags probably apply just as much as the logic-puzzle one? $\endgroup$ – Brent Hackers Jun 7 '16 at 20:54
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My understanding is that

The [one] stone object can't weigh one pound because one stone weighs 14 pounds!

•Write all the digits of pi on this piece of paper

The digits that make up Pi is infinite (impossible then?) NO! you can just write "0123456789"?

•Hold in front of me a baby that is exactly two days old.

A baby can surely be exactly 2 days old if only for a moment.

•Bring me a metal object that weighs exactly one kilogram.*

A 1kg metal weight?

•Bring me a glass filled with something other than water that is exactly the same density as water.

Struggled with this one because as BmyGuest (+1) said water doesn't have a specific density. It changes based on it's contents. Salt water is water and yet more dense than fresh water, so maybe pick a liquid with a density somewhere in that range? a mixture of d<1 and d>1 liquids should do the trick according to klm123. Thanks (+1).

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    $\begingroup$ "metal object that weighs exactly one kilogram" can be the weight itself?(one which is used in weighing scale?) $\endgroup$ – smriti Jun 7 '16 at 7:34
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    $\begingroup$ @MikeM. that isn't what I was going for, and I added a note to clarify. Thanks. $\endgroup$ – user21939 Jun 7 '16 at 7:37
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    $\begingroup$ Water density is not constant. (Depends on pressure & temperature) $\endgroup$ – BmyGuest Jun 7 '16 at 7:38
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    $\begingroup$ What is the problem with water? just make a mixture of d < 1 and d > 1 liquids. You can make it go from ~0.9 density to ~1.1 density just in front of the man, exactly like the child age. $\endgroup$ – klm123 Jun 7 '16 at 7:52
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    $\begingroup$ @klm123 in Britain a "stone" is a unit of mass weighing 14 pounds, so the idea is that you couldn't have a stone weighing one pound. However, I don't think this really works. "A stone object" isn't naturally read as an object weighing one stone, and anyway, nothing the man said requires you to interpret it this way. $\endgroup$ – user21939 Jun 7 '16 at 8:03
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Is it:

Glass

because:

baby - hold around the exact time
metal - scales weigh things and can be made from metal and can weigh exactly $1kg$
stone - perfectly possible
$\pi$ - base dependent so $0,1$

and so:

the speaker said 'Bring me a glass, containing something other than water, that is exactly the same density as water.' Note the commas, and glass cannot have the same density as water.

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  • $\begingroup$ Ha. Clever. I like this answer better than the correct solution! +1 $\endgroup$ – Brent Hackers Jun 7 '16 at 9:12
  • $\begingroup$ I would say the weakness here is that you allow creative interpretation of some sentences to solve them (stone, metal, pi) and yet force a particular interpretation of the other challenge to say it's not possible. But overall +1 for some interesting creative ideas. $\endgroup$ – user21939 Jun 7 '16 at 10:42
  • $\begingroup$ You answer does create the possibility that all might be achievable. $\endgroup$ – user21939 Jun 7 '16 at 10:44
  • $\begingroup$ I wouldn't consider a punctuation trick to be in the spirit of the puzzle. $\endgroup$ – Tony Ennis Jun 7 '16 at 13:11
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    $\begingroup$ Normal plate glass has a higher density, but aerogel is also glass with much lower density, so a suitable composite would have neutral density. $\endgroup$ – Pete Kirkham Jun 8 '16 at 12:52
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I am not quite satisfied with any of the explanations, so, here's my own interpretation...

You cannot hold in front of them a baby that is two days old.

Reasoning

Reading this quite literally:
"I'm sorry", you say, "but that is impossible. I can complete four, but there is one I cannot do."
So clearly, #4 can be completed (Glass containing something other than water)... but #1 cannot! (Which in the order you wrote them, is the one about the baby).

"Keep in mind that this puzzle was spoken, not written down."
The mention of speech further suggests that the speaker may have meant to say "I can complete [number] four, but there is [number] one I cannot do." Often words are omitted in speech.

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  • $\begingroup$ Interesting idea. $\endgroup$ – user21939 Jun 7 '16 at 13:10
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This is a long shot, but the task I can't do is:

Hold in front of me a baby that is exactly two days old.

Because:

The age will not be exact, it will increase minute by minute.

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  • $\begingroup$ i beg to differ - you can hold the baby for a couple of minutes as it's turning exactly 2 days old... $\endgroup$ – Ben Jun 7 '16 at 7:25
  • $\begingroup$ Nope. While you are correct about the issue for that task, there is a workaround. As Ben stated. $\endgroup$ – user21939 Jun 7 '16 at 7:25
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    $\begingroup$ Oh,i thought the age will increase constantly, like 2 days and min, 2 days and 2 min..... and as title suggest "infinite precision" $\endgroup$ – smriti Jun 7 '16 at 7:26
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How about:

stone, because a stone (unit of weight) weights 14 pounds, not one.

because:

you can hold a baby that is less than 2 days old, and wait awhile. There are international kilogram standards that are made from metal. The metal defines the kilogram. Bring a glass of ice, and wait for it to melt. It is trivial to literally write "all the digits of pi" on a piece of paper. That only leaves the stone as being impossible.

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  • $\begingroup$ Nothing the man said requires you to interpret "stone object" in this way. Also, ice is water. $\endgroup$ – user21939 Jun 7 '16 at 8:13
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    $\begingroup$ According to engineeringtoolbox.com/density-materials-d_1652.html, phosphate fertilizer has a density of 961 kg/m3. Limestone dust has a density of 1089. Mix them in a 2:1 ratio and it's a density of a little over 1000. This is the same density as some water somewhere at some temperature. "Spring water" is water. The stuff that comes out of your tap is water. The stuff that flows in rivers is water. Seawater, arguably, is water. None of it has a density of exactly 1,000 kg/m3. $\endgroup$ – Hugh Meyers Jun 7 '16 at 8:31
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How about:

The second one. Kilogram is a unit of mass. You weigh a kg-wt.
The first can be done by waiting, as most others have suggested.
The third, I have yet to find a conclusive answer. Suggests? Or we go with @Jon's answer, "It's perfectly possible".
Fourth. Gases are fluid, with no specific volume. Take an empty glass, and compress the air, until it matches the density of water. Assume that the glass can withstand it.
Fifth. As the others have suggested, either "0123456789", or literally, "All the digits of pi". Or... @Jon's awesome answer. 0,1, as answer is base dependent.

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I can do all but four, for I have nothing to write with. If I write with the baby, it will no longer be exactly 2 years old. With either the metal or stone it will become smaller as I use it. To use the glass or the liquid within would again diminish the glass and it shall leak or the liquid will evaporate.

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