# Deceptively easy math word problems for high school kids **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [February 2, 2012, 7:31pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563 "2012-02-02T19:31:57Z")\ **Posts on this page:** 20\ **Page:** 7
**Author:** ![Gedd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gedd/32/4938_2.png) [@Gedd](https://boards.straightdope.com/u/Gedd)\ **Post date:** [February 6, 2012, 5:18pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/121 "2012-02-06T17:18:52Z")
> [@Quercus](#): > > “As I was going to Saint Ives…” . . . I came to a junction and there were two guys. One guy always lied and one always told the truth. Wait, that one isn’t a math problem. ---
**Author:** ![Michael63129](https://avatars.discourse-cdn.com/v4/letter/m/3da27b/32.png) [@Michael63129](https://boards.straightdope.com/u/Michael63129)\ **Post date:** [February 6, 2012, 5:39pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/122 "2012-02-06T17:39:57Z")
> [@indian](#): > > Using algebra, yes one can slip a knife. > > D1= diameter of first circle > D2=diameter of 2nd (big) circle > > C1= circumference of 1st circle > C2= circumference of 2nd (big) circle > > C2=C1+1 > > The space between the spheres will be( D2-D1)/2 > > D2-D1= [(C1+1)/pi-C1/pi)]=[C1+1-C1]/pi=1/pi > > Distance between spheres is =(1/pi)/2= 1/(2xpi)= 1/6.28=0.15 foot= 4.8 cms > > Yes, the problem is deceptive. When I first saw that problem, the first thing I did was calculate the circumference of the Earth in feet (~25,000 miles x 5280 = 132,000,000 feet), then divide 1 by the circumference to get 0.000000008 feet (rounded, about 2.3 nanometers), or in other words, impossible with any realistic knife. Upon reading further replies, including yours, I tried it out myself with a tape measure on various circular objects and found that it was indeed possible. Just hard to imagine that such a small relative change could cause such a large gap when distributed over the entire Earth. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [February 6, 2012, 5:42pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/123 "2012-02-06T17:42:23Z")
> [@MaxTheVool](#): > > Assume the earth is a perfect solid sphere. Construct a metal band all the way around the earth’s equator, snug with the ground. Now increase the length of that band by 1 foot, distributed evenly. > > Would it be possible to slip a knife blade between the band and the earth’s surface? Will putting the knife on the ground between two of the members’ feet work? ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [February 6, 2012, 5:46pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/124 "2012-02-06T17:46:59Z")
> [@Frylock](#): > > Will putting the knife on the ground between two of the members’ feet work? Most metal bands would kick you in the teeth if you tried. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [February 6, 2012, 5:54pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/125 "2012-02-06T17:54:47Z")
> [@Musicat](#): > > It seems to me that that will never equal 100, but come infinitely close. I’m amazed this didn’t happen til page three. 😉 ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 6, 2012, 6:30pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/126 "2012-02-06T18:30:41Z")
> [@Baffle](#): > > That’s the ‘gut feeling’ mistake. Wikipedia has [an article](http://en.wikipedia.org/wiki/.999) on the number, but the proof that convinced me was simple: > > 1/3 = .333 repeating > 2/3 = .666 repeating > > 1/3 + 2/3 = 3/3 = 1 > > .333 repeating + .666 repeating = .999 repeating = 1 The best proof I’ve seen comes from this board. There are no other numbers between .999… and 1. Therefore, they are the same number. ---
**Author:** ![Sam\_I\_Am](https://avatars.discourse-cdn.com/v4/letter/s/e495f1/32.png) [@Sam\_I\_Am](https://boards.straightdope.com/u/Sam_I_Am)\ **Post date:** [February 6, 2012, 9:54pm UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/127 "2012-02-06T21:54:27Z")
> [@Inner\_Stickler](#): > > Do you also feel frustrated when you begin a recipe at step 2 and your pie never cooks because you didn’t preheat the oven in step 1? The point of the test isn’t to trip students up, it’s to underline the importance of reading all the instructions before doing anything and hopefully to go about it in an amusing way. If you did poke holes in your paper and so on but learned the lesson about instructions, then you didn’t fail the test at all. Regardless of whether it is an exam, a recipe, or a programming language that involves numbered lines of code, reading the whole thing before you start does not override the convention that numbered steps or questions are executed in number order. ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 7, 2012, 12:29am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/128 "2012-02-07T00:29:00Z")
> [@Michael63129](#): > > When I first saw that problem, the first thing I did was calculate the circumference of the Earth in feet (~25,000 miles x 5280 = 132,000,000 feet), then divide 1 by the circumference to get 0.000000008 feet (rounded, about 2.3 nanometers), or in other words, impossible with any realistic knife. Upon reading further replies, including yours, I tried it out myself with a tape measure on various circular objects and found that it was indeed possible. Just hard to imagine that such a small relative change could cause such a large gap when distributed over the entire Earth. Upon first reading of the problem, I thought it is not possible. Then I tried algebra. It is interesting to note that C1 & C2 cancels out. That means t **his will hold true for any sphere, where circumference is increased by 1 foot.** ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 7, 2012, 12:35am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/129 "2012-02-07T00:35:46Z")
> [@Gedd](#): > > . . . I came to a junction and there were two guys. One guy always lied and one always told the truth. > > Wait, that one isn’t a math problem. You can ask the second guy, “what would the first guy say the math problem is”? 😉 ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [February 7, 2012, 12:38am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/130 "2012-02-07T00:38:02Z")
> [@Michael63129](#): > > When I first saw that problem, the first thing I did was calculate the circumference of the Earth in feet (~25,000 miles x 5280 = 132,000,000 feet), then divide 1 by the circumference to get 0.000000008 feet (rounded, about 2.3 nanometers), or in other words, impossible with any realistic knife. Upon reading further replies, including yours, I tried it out myself with a tape measure on various circular objects and found that it was indeed possible. Just hard to imagine that such a small relative change could cause such a large gap when distributed over the entire Earth. The problem is that you had calculated an irrelevant quantity. The ratio of added circumferential length : existing circumferential length (1 foot : circumference of Earth) has nothing to do with whether you can slip a knife under; the fact that 0.000000008 feet is very small is of no relevance. Slipping a knife under is a question of the added radius, not the percentage increase in circumference. And as we all know, radius is proportional to circumference, so adding 1 foot to circumference adds 1 foot/(2π) to radius, no matter how big or small the existing circumference is in comparison to 1 foot. ---
**Author:** ![Pops1963](https://avatars.discourse-cdn.com/v4/letter/p/9de053/32.png) [@Pops1963](https://boards.straightdope.com/u/Pops1963)\ **Post date:** [February 7, 2012, 12:38am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/131 "2012-02-07T00:38:48Z")
How many doors does a chicken coop have? 2 if it had 4 it would be a chicken sedan ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [February 7, 2012, 12:46am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/132 "2012-02-07T00:46:35Z")
> [@Indistinguishable](#): > > The problem is that you had calculated an irrelevant quantity. The ratio of added circumferential length : existing circumferential length (1 foot : circumference of Earth) has nothing to do with whether you can slip a knife under; the fact that 0.000000008 feet is very small is of no relevance. Also, keeping track of units, the ratio 1 foot : circumference of Earth is a dimensionless 0.000000008, not 0.000000008 feet. Which also shows it to be irrelevant; you can’t compare the width of a knife to a dimensionless value. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 7, 2012, 12:55am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/133 "2012-02-07T00:55:22Z")
> [@Indistinguishable](#): > > Also, keeping track of units, the ratio 1 foot : circumference of Earth is a dimensionless 0.000000008, not 0.000000008 feet. Which also shows it to be irrelevant; you can’t compare the width of a knife to a dimensionless value. Could you tell me what you mean by dimensionless here? ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 7, 2012, 1:03am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/134 "2012-02-07T01:03:55Z")
> [@TriPolar](#): > > Could you tell me what you mean by dimensionless here? Both dimensions are expressed in " foot". When you divide 2 quantities, where both are expressed in foot, the result will be just a number without a dimension. Example: 300 feet/ 25 feet= 12 not 12 feet. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 7, 2012, 3:02am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/135 "2012-02-07T03:02:37Z")
> [@indian](#): > > Both dimensions are expressed in " foot". When you divide 2 quantities, where both are expressed in foot, the result will be just a number without a dimension. > > Example: 300 feet/ 25 feet= 12 not 12 feet. Ok, thanks. Now I understand. ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [February 7, 2012, 4:48am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/136 "2012-02-07T04:48:30Z")
Look at this book: [Aha!: a two volume collection](http://books.google.com/books/about/Aha.html?id=EV2y4z95_KQC) by Martin Gardner. There are a lot of candidates there, even in the abridged preview version. One tricky problem is on page 70, “Bipeds and Quadrupeds”. If you see something interesting that is just partially there, I have both Aha! volumes and can supply the missing parts. ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 7, 2012, 5:41am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/137 "2012-02-07T05:41:56Z")
Melons are 99% water and 1% "melon"y matter(let us call it pulp) by weight. A 100 Pound melon is dried in sun for a couple of days.The dried melon is 98% water. What is the weight of the melon now? ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [February 7, 2012, 5:51am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/138 "2012-02-07T05:51:11Z")
> [@indian](#): > > Melons are 99% water and 1% "melon"y matter(let us call it pulp) by weight. > > A 100 Pound melon is dried in sun for a couple of days.The dried melon is 98% water. What is the weight of the melon now? 50 pounds? ---
**Author:** ![Indian](https://avatars.discourse-cdn.com/v4/letter/i/c0e974/32.png) [@Indian](https://boards.straightdope.com/u/Indian)\ **Post date:** [February 7, 2012, 5:53am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/139 "2012-02-07T05:53:40Z")
Yes! ---
**Author:** ![KKKK](https://avatars.discourse-cdn.com/v4/letter/k/48db29/32.png) [@KKKK](https://boards.straightdope.com/u/KKKK)\ **Post date:** [March 19, 2012, 7:08am UTC](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563/140 "2012-03-19T07:08:00Z")
> [@batsto](#): > > Anyone know any tricky word problems that a high school kid could be easily fooled by? I’m not looking for difficult math, but rather problems where the wording misleads the student. > For example, this one gets a surprising number of high school kids: > > If it takes 10 minutes to cut a board into 2 pieces, how long does it take to cut it into 3 pieces? > > For some reason, a lot of high school kids set up a proportion and figure it takes 5 minutes per piece, so they arrive at 15 minutes as an answer. > > Does anyone have any similar kind of trick problems of that nature? What is the product of (x-a)(x-b)(x-c)…(x-z)? Since one of the elements of the series is (x-x), i.e., zero, the answer is zero… [Previous page](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563.md?page=6) [Next page](https://boards.straightdope.com/t/deceptively-easy-math-word-problems-for-high-school-kids/611563.md?page=8)