7 ms·
They're interesting to adults, too! Simple enough that it feels like you should be able to blurt out the answer, I'm more than twice the maximum recommended age
by LeifCarrotson 5y ago
They're interesting to adults, too! Simple enough that it feels like you should be able to blurt out the answer, I'm more than twice the maximum recommended age and a professional engineer, but (at least for me) it takes some thought. The top recommended three:
> 1. Masha was seven kopecks short to buy a first reading book, and Mishalacked one kopeck. They combined their money to buy one book to share, but even then they did not have enough. How much did the book cost?
> 3. A brick weighs one pound and half the brick. How many pounds does the brick weigh?
> 13. Two volumes of Pushkin, the first and the second, are side-by-side on a bookshelf. The pages of each volume are 2 cm thick, and the cover – front and back each – is 2 mm. A bookworm has gnawed through (perpendicular to the pages) from the first page of volume 1 to the last page of volume 2. How long is the bookworm’s track?
I do take objection to the answer to question 13 - the author seems particularly set on one way of loading the bookshelves as correct.
- sokoloff 5y ago1. Depends on whether kopecks are divisible into a smaller monetary unit or not. If they are divisible into 100 units, I believe the answer is "anywhere between 7.00 and 7.99 kopecks". (Problem #2 requires kopecks to be divisible.)
- deleted 5y ago[deleted]
- ekster 5y agoA kopeck is like a cent (1/100th of a ruble).
- valbaca 5y agoThey're not. It's like a penny. Sure you may have parts of cents like with gas, but for girls buying books, it's the lowest currency value.
- Symbiote 5y agoLong ago, many currencies had more divisions than they do now. The penny of GBP came in quarter pennies (farthings) until 1950. Half US-cent coins were made until 1857.
- haxiomic 5y agoWorks even if Kopecks are divisible: say the books value is 7.5, Mash must have 0.5 (7.5 - 7) and Misha 6.5 (7.5 - 1), however now when you combine them they sum to exactly 7.5 not less than, the only way to arrive at less than is if Masha has 0. So its always exactly 7
- LeifCarrotson 5y ago6.5 plus 0.5 is 7.0, they don't add up to exactly 7.5.
- gabagool 5y ago6.5 + 0.5 is 7.0, not 7.5, so that should be valid. The book's cost can lie anywhere between [7, 8).
- haxiomic 5y agoRight on the original typo, but still not convinced, I’ve rephrased to original to try to be clearer
- thaumasiotes 5y ago> say the books value is 7.5, Mash must have 1.5 (7.5 - 7) and Misha 6.5 (7.5 - 1), however now when you combine them they sum to exactly 7.5 not less than There are several problems with this: - 7.5 - 7 is 0.5, not 1.5 - 1.5 + 6.5 is 8, not 7.5 - 0.5 + 6.5 is still less than 7.5 The problem specifies that 2x - 8 < x. There is no way to constrain this to the specific solution x = 7. Everything would work fine if the book cost -2.6 kopecks.
- haxiomic 5y agoThank you :) I’m being very clueless today
- deleted 5y ago[deleted]
- culebron21 5y agoBefore 1917, they were divisible into 4 polushkas.
- rjp0008 5y ago> (Problem #2 requires kopecks to be divisible.) Does it? Did I fail at problem 2? I got: Bottle + cork = 10 Bottle = 9cork bottle/9 = cork 9(bottle + bottle/9) = 9(10) 9 bottle + bottle = 90 10 bottle = 90 bottle = 9 9 = 9cork 1 = cork
- sokoloff 5y agoI read the second statement ("the bottle itself is 9 kopecks more expensive than the cork.") as: Bottle = 9 + Cork Your statement (Bottle = 9 * Cork) would be "the bottle is 9 times as expensive as the cork". I solve it to: Bottle = 9.5 Kopecks. Cork = 0.5 Kopecks.
- amativos 5y agoI think part of the point of this brochure is to think about the problems intuitively in the context they are presented. So in the first problem it's just kids trying to buy their first book, it would be silly to think Masha had a fraction of a kopeck (assuming you understand what a kopeck is, I really think it should have been translated as cent) and that the answer could be in range [7, 8). This may be what he talks about when he says that many academics fail at these problems. Similarly, in problem #2 the cork indeed costs 0.5 kopecks but in this case we're just thinking about cost conceptually, not in terms of how much money a person actually has on hand.
- sokoloff 5y agoIndeed, but it likewise seems intuitively reasonable to think that a book costs much more than 7 cents (or 7 times whatever the atomic unit of currency is) and that over 100 times the atomic unit is more reasonable.
- Negitivefrags 5y agoWhat is your objection to question #13? I suppose the question doesn’t mention that volume 1 is on the left and volume 2 is on the right but I guess that would be assumed by any speakers of left to right languages.
- frostirosti 5y agocould also be the case that the two volumes are empty, ie have no pages
- Jtsummers 5y agoThe problem statement gives us that there are 2cm of pages in each book. So they are not empty. The confusion is in which order the books would be on the shelf, and consequently which direction the bookworm would be moving and through what.
- valbaca 5y agowhat book has no pages? Also the problems states: > The pages of each volume are 2 cm thick
- thaumasiotes 5y agoThe pages would be less than 20mm thick in that case.
- deleted 5y ago[deleted]
- thaumasiotes 5y ago> I suppose the question doesn’t mention that volume 1 is on the left and volume 2 is on the right but I guess that would be assumed by any speakers of left to right languages. The answer is supposed to be 4mm; the only way for that to work if volume 1 is on the left is for the bookworm to gnaw its way out of the book from v.1.p.1, cross the outside of the two books without gnawing anything until it reaches the back cover of volume 2, and then gnaw its way through that cover to reach the final page of volume 2. I don't think that's what the question has in mind. The point of being a bookworm is that you don't leave the book. So the answer would appear to require that volume 2 is shelved in front of volume 1. I don't know why that would be the case.
- culebron21 5y agoMy answer to #1 is less than 8 kopecks, and Masha has less than one. There's a problem: nowadays kopecks are the minimal unit of currency. Either it means you have to think of the old Imperial money units (polushka, 1/4 of kopeck), or think of fractional amounts of money.
- bencollier49 5y agoI assumed kopecks were pennies. If Misha needs one, and Masha doesn't have enough to give her one, than Masha must have none. So the answer follows from that.
- culebron21 5y agoBut naturally, at first you assume the numbers are natural. :)
- throwaway744678 5y agoWell, yes, otherwise you'd have an infinite number of solutions.
- colinmhayes 5y agoHow can they combine their money if one of them doesn't have any?
- bencollier49 5y agoCommunism?
- sethammons 5y agoOk. I literally laughed out loud.
- deleted 5y ago[deleted]
- valbaca 5y ago> side-by-side on a bookshelf Seems pretty explicit to me
- macintux 5y agoWhich volume is to the left? Thus the ambiguity.
- valbaca 5y ago> A bookworm has gnawed through (perpendicular to the pages) from the first page of volume 1 to the last page of volume 2. How would a worm eat perpendicular to the pages and go from the first page of volume 1 to the last page of volume 2? It can only be vol1->vol2
- deleted 5y ago[deleted]
- thaumasiotes 5y ago> How would a worm eat perpendicular to the pages and go from the first page of volume 1 to the last page of volume 2? Sorry, what is the question supposed to be? You're positing a contradiction between two facts: - The worm's path is perpendicular to the pages. - The worm's path begins at the first page of volume 1, and ends at the final page of volume 2. What's the contradiction?
- scratcheee 5y agoThe bookworm could have moved right to left from volume 1 to volume 2. Assuming the spines are facing out, the books are right-way up, and volume 2 is on the left of volume 1, then the answer would be 44mm.
- SamBam 5y agoWhile the answer does assume that V1 is on the left, there's no contradiction in your statement. If V2 happened to be on the left, it would still be perfectly logical for "a worm eat perpendicular to the pages and go from the first page of volume 1 to the last page of volume 2." They would simply have to go through more pages.
- dahfizz 5y ago> A brick weighs one pound and half the brick. How many pounds does the brick weigh? I am a native english speaker and am having a hard time parsing this one. The only sane interpretation I can think of is that one pound + half the brick = the whole brick. EDIT: I think the reason it is so confusing to me is because "and half the brick" sounds like (the start of) an independent thought. "A brick weighs one pound and half the brick was painted yellow". This version is much clearer, IMO: "A brick weighs one pound plus half a brick". Maybe there is a fear that wording the problems too clearly makes the solution obvious.
- wizzwizz4 5y agoCorrect.
- deleted 5y ago[deleted]
- idownvoted 5y agoInteresting. There seem to be a lot of native speakers here that have problems with the grammar, while I – and assume many other non-native speakers – don't.
- bumbledraven 5y agoHere’s a way to use algebra to grind out the solution to #1 with no particular insight needed. Assume that prices and the amount of kopeks a person has are both represented by nonnegative integers. Let A be Masha’s kopeks, let I be Misha’s kopeks, and let B be the price of the book. We are given the following: A = B - 7 (1) I = B - 1 (2) A + I < B (3) Substituting (1) and (2) into (3) yields B - 7 + B - 1 < B (4) This simplifies to B < 8 (5) B = 7 satisfies (5) and, from (1) and (2), implies that A = 0 and I = 6, which together satisfy the givens (1), (2), and (3). So B = 7 is a solution. Furthermore, we cannot have B < 7 or else (1) would imply A < 0, contradicting the assumption that our variables are represented by nonnegative integers. So B = 7 is the only solution.
- nostoc 5y agoIt's also quite easy to do intuitively. Since Misha is missing only one kopeck, had Masha owned any amount, the sum would have been enough to buy the book. Therefore, Misha doesn't have any money, and the price book is what Misha is missing : 7 kopecks.
- bumbledraven 5y agoThat’s a nice approach. (It’s the same one given by bencollier earlier: https://news.ycombinator.com/item?id=27885681 https://news.ycombinator.com/item?id=27885681). I regard it as requiring a bit of insight, as opposed to my approach, which is more like grinding gears to reach a conclusion.
- lordnacho 5y agoThis is one of my main observations growing up with math: it's the moments of beauty and elegance that are the most exciting, but the grinding gears thing is also a necessity. They complement each other. For instance when you're just learning the basics there's a lot of these "wow what an insight" but over time you figure out that people have distilled it into a mechanical procedure, which also has some attraction to it. Something like quadratic equation turns the search for a pair of numbers that add up some one thing and multiply to another into a simple formula. You then use that mechanism to build ever more elaborate ones.
- BeFlatXIII 5y agoThese problems are worded to be deliberately confusing, especially #1. Is it a translation issue or are they worded because the math itself is too obvious once the wording has been deciphered?