## Answers to the proveyourlogic.com test (Spoilers) (Update: Now with explanations)

December 20th, 2007

Update: Thanks to all the people who have linked to this page. Here’s a list of linkbacks. I’ll expand it as I discover new pages linking back to me.

These are the correct answers to the “Prove your logic” test on proveyourlogic.com. It’s not really an iq test, but it took some some thinking nevertheless. I wonder who’s behind the test anyway.

```1) money (or nothing)
2) t
3) first
4) five
5) anchor (or net)
6) thursday
7) water
8) 2
9) 6
10) Gregory
11) 999
12) 3
13) 2
14) mother
15) maid
16) m
17) e
18) 13
19) 28
20) Everest
21) 25
22) August
23) 8000
24) 35
25) 59 (Last question)
```

Explanations to some of the answers may come at a later date. Because of the lare number of new visitors because of this post, I’ve decided to write a tutorial for the test with explanations for each question.

1. If you put the word money (Or the word nothing) into the sentences, they’ll be correct. (According to some logic)
I don’t personally agree with the idea that “nothing is better than god”, being an atheist. (Unless the sentence is read as believing in nothing is better than believeing in god)
Also, the sentence 2 and 3 become flawed if you insert “nothing”, because of a double negation.
But nevertheless, these are the working answers for that question.
2. The first letters in the English words for the numbers 1-10 (One, two, three,… ten)
3. The date July 20th, 1929 occured before the Second World War, thus there was nothing such as a “First World War”, there was only “The world War”. (Or rather The Great War, as it was called in most of the world at the time. Thanks Vince for noticing.)
4. Count the number of letters inthe words. For seven, this is obviously 5.
5. An anchor is something you throw in the water when you need to use it, and then pick up when you set asail again.
6. Since the rules don’t allow that they both lie on the same day, (Yesterday) one of them must be lying today. Thursday is the only possible day. (The hunter told the truth yesterday, but is lying today, so he says he was lying yesterday. The fisherman is telling the truth when he’s saying he lied yesterday.)
7. No matter how much dry food you take with you, you will die without water.
8. I was later told that the purpose of this riddle was to count the number of loops in the digits. So the values of the digits on the left side are: 0=1, 6=1, 8=2, 9=1, all other digits=0. Also note how the avoided the digit 4 on the left side, since it can be written in either closed or open loop.
However, my way of solving it was a more bruteforce way, where I looked at the equations as a linaer equation system where every number on the right side is the symbol for an unknown variable. So I could easily read out zero-valued symbols from the equations with 0 on the right side. (With the assumption that every symbol could only take on a 0 or positive integer value) So from the given equations 2222=0, 5555=0, 1111=0, I could deduct that 2=5=1=0. Then from a little work I was able to see that 8=2 and I was able to get the answer.
9. I actually don’t get why this question is supposed to ne hard but, anyway, there are 6 F’s in that sentence.
10. The 4th kid is not named after a month. The key point here is the sentence “His mother have 4 kids” (Bad grammar as always) It says Gregory is one of the kids, and since the other three are mentioned in the next sentence, he must be the 4th one.
11. If there are 1000 pages, and one tells the truth, consequently 999 pages are lying. And that is what page 999 says.
12. The tricky part here is how the books are placed. The riddle assumes they are placed as 1-2-3. this means that the bookworm starts at page 1, vol 1, will eat its way through the cover of vol 1, the whole vol 2, the back cover of vol 1 and then stop at the last page of vol 3. That’s 2 covers and 1 whole book, which gives 2*0.25+2.5=3.
13. 15 lions that haven’t eaten for 5 years would be very hungry if it wasn’t for the fact that they are dead.
14. Since his father was dead, the doctor who said “He is my son” must be his mother. This riddle seems bit out of place, since the whole story is meant to describe some sort of almost ancient civilization. :p
15. The killer is the maid, with the motivation that there’s no mail in Sundays. Well, there are probably a lot of countries there is mail delivery in Sundays. They probably picked this one from a Sherlock Holmes book or something.
16. The letter m appears once in the word minute, twice in moment but nowhere in the word years.
17. This message:

Uif cfhjoojoh pg fufsojuz
uif foe pg ujnf boe tqbdf
uif cfhjoojoh pg fwfsz foe,
Boe uif foe pg fwfsz qm qmbdf.

is coded with a simple caesar cipher (Rot1) “Page -1″ also gives a clue about this. By shifting every letter one step to the left you get:

The beginning of eternity
The end of time and space
The beginning of every end,
And the end of every place.

Again, they’re looking for a letter, namely e, since eternity begins with e etc.
However, I don’t get the point of the left sheet, “P, page +3″ Shifting P with +3 gives S, which is no help. Maybe they’re referring to the answer to the previous question, (M shift +3 = P)

18. Classic combinatorial style question. There are 6 pairs of black boots and 6 pairs of brown boots. If you pick 12 boots and have maximum bad luck, you’ll get 6 brown lefts and 6 black lefts. But at that point if you pick another shoe, it is guranteed to be either a black or brown right shoe. In other words, 13 is the lowest number of boots you need to pick to be guaranteed to get a mathing pair.
19. The snail effectively climbs one foot a day. On day 27 it climbs up from 26 feet to 29 feet, but slips back to 27 feet. But on day 28, it climbs from 27 feet to 30 feet, and doesn’t need two more days to reach the top.
20. Captain obvious says: Before Everest was discovered, Everest was still the tallest mountain. Yet another riddle that’s a bit out of context for the story.
21. Let’s read the story backwards.Assume August left with as little as possible:
August took 1 fish, (A third) and left 2. (Two thirds) Before that, he threw away 1 fish.
In other words, there were 4 fish when he arrived at fishplace.

So, June left 4 fish, (Two thirds) and took 2. (One third) Before that, he threw away 1 fish.
In other words, there were 7 fish when he arrived at fishplace.

So, April left 7 fish, (Two thirds) … But since 7 is not divisible by 2, the assumption was wrong, let’s start allover.

Same error happens if we start out with takes 2, leaves 4.

August took 3 fish, (A third) and left 6. (Two thirds) Before that, he threw away 1 fish.
In other words, there were 10 fish when he arrived at fishplace.

So, June left 10 fish, (Two thirds) and took 5. (One third) Before that, he threw away 1 fish.
In other words, there were 16 fish when he arrived at fishplace.

So, April left 16 fish, (Two thirds) and took 8. (One third) Before that, he threw away 1 fish.
In other words, there were 25 fish when he arrived at fishplace.

Which is the answer they expect. However, that answer is not unique. In fact any value given by the function:
f(i)=27*i-2 [Where i>0 and is an integer]
is a valid number of fish to start out with. (25, 52, 79, 106…) However, they only accept 25 as an answer. They could’ve avoided this ambiguity by defining the number fo fish that were left when all three brothers were done. But they didn’t.

22. Let’s build a truth table where Gregory, April, August and June are represented by the letter A-D (And their actions by the letter a-d, so a means “Gergory broke the window” for example) I’m using a C-style notation, so, ! means not.
 A B C D 1st time !a !b b b 2nd time d !c !b !d

We now have two useful rules here: Two people told the truth and two people lied. We have a depency here: if D tells the truth, so must C; if D lies, so must C. So we have two possible outcomes. Here’s the truth table redrawn for the two outcomes, with things that are true (Áccording to the assumption) marked in bold.

 Assumption 1 A B C D 1st time !a !b b b 2nd time d !c !b !d Assumption 2 A B C D 1st time !a !b b b 2nd time d !c !b !d

In assumption A, we get a lot of contradictions, following the statement, both A, B and D would be guilty. On the other hand, in assumption B we get a sound result: A, B and D are innocent, and C is guilty. (C=August)

23. This one requires some mathematical reasoning. The sum of every row is a sum of numbers:
s(n)=x1+x2+x3+…+xn
… for row n. Let’s not care about the exact value of those numbers for now, and just think of them as symbols. Instead look at the average value of every row which is
a(n)=(x1+x2+x3+…+xn)/n
or:
a(n)=s(n)/n
… for row n, since row n contains n elements.
This is something we can use, because we can get the average for every row easily. the average for every row is the middle number (Or the sum of the two middle number if a row contains an odd number of numbers) The averages for the displayed rows are:
1,4,9,16,25,36
Anyone who knows math should recognize these numbers as squares. In other words we can also express the aerage function as:
a(n)=n2
By setting up the two expressions for the average function as an equation:
a(n)=s(n)/n=n2=a(n)
we get:
s(n)=n3
For row 20 this is 203=20*20*20=8000
24. The problem here is that the triangles overlap. However, you can make the calculation simpler by using the symmetry, by choosing a section and counting the triangles in that section and multiplying by 5. The number of subtriangles is 7, so the total number of triangles is 5*7=35.
Here’s a possibly annoying GIF animation showing the 7 subtriangles.
25. The flood will double its size every day. So if half the city is flooded after 59 days, obviously if you double that, the whole city will be flooded after 60 days.

If you came here via a search engine, feel free to browse the rest of my site or listen to my Gameboy music.

Update: Thanks to this page there are OVER 9000 people on the “list of the people who have proved their logic”. (Don’t blame me. They are the ones who don’t know the difference between proven and proved, not me)

Raspunsuri la proveyourlogic. Raspunsuri la proveryourlogic. Raspunsuri la powerlogic.

### 49 Responses to “Answers to the proveyourlogic.com test (Spoilers) (Update: Now with explanations)”

1. Optimus says:

Nice!

Although usually I am in such a hurry to spend more time on such tests that I see the solutions. Half of the questions I could answer easilly alone but I am waiting your explanations for few other answers I am still puzzled about. When I was about to loose I checked your answers and wondered and wrote these one in order to not start from the beginning.

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3. reve says:

thanks for the explanations!! it’s great!
i found this website after the test… just realize that can “cheat” is some case… haha~

by the way, no.5 i put “net” which is also accepted!

4. nitro2k01 says:

Thanks for the comment, reve. I’ve updated the page.

5. Lisa says:

A lot of these were riddles I heard when I was younger, and you’re right - they don’t fit well with the story. The bad grammar was driving me CRAZY!! (”How *much* inches”, etc)

Number 9 though you said you didn’t get why it’s supposed to be hard - me either haha… but I actually read online a long time ago that studies have shown only a small percentage of people get that correctly (hooray for us!) because the F in “of” makes the “V” sound and the brain for a lot of people naturally skip over those Fs in the sentence.

6. Czarena says:

#24 is incorrect, though it is the answer the game thinks is correct. Using the gif as reference, the reverse of the orange triangle is omitted from the count (or the compilation of red, green and yellow triangles)

7. nitro2k01 says:

Czarena: Damn it! You’re so right about that! Honestly, I’m more disappointed at myself than at the creators of the quiz for not seeing it.

8. nitro2k01 says:

Czarena: At a closer inspection, they’re not wrong, but I am. I forgot to include the opposite of the orange triangle. However, the yellow or the green triangle is incorrect. (Either one of them) They are the same triangle in different subgroups, so it’s a duplicate.
One forgotten+one too much=still 7 subtriangles.
But the error in the image is fixed now. The green triabgle is now changed so that it covers the missing big triangle.

9. Czarena says:

ok now I feel silly, you are correct only the yellow or green triangle can count - so the total count is correct still I’m not seeing the update in the image yet though (not picking, just so you know)

10. Peter Smith says:

Thanks

11. Some idiot says:

you really are an idiot. putting answers to such a test on a website/blog is like cheating in online games -> everyone who got through it without cheating will find himself in the finisher’s list together with thousands of cheaters. because of whom? because of you!

12. nitro2k01 says:

I’m no more idiotic than the people who made that test. They put it together with little effort by picking riddles from everywhere and trying to make a fancy story out of it, but failing because the riddles are out of place and the grammar is so bad you want to puke. They are idiots for doing such a badly designed test.
And it’s not like their finisher’s list is the Mensa membership list.

In the end of the day they published that test for the same reason that I published the answers: To get web traffic. I’m not the least ashamed for publishing these answers. If they had made a test that I had felt respect for, the situation might have been different.

13. laszlo says:

20th question, they say the tallest mountain in the world. We don`t know that , and probably wont know it ever. But the tallest mountain we know of is the Olympus on the Mars, 24 km.
And for the 21st question I got all the other answers except the first one.

14. nitro2k01 says:

The test says “The tallest mountain in the world”. “The world” is usually defined as the earth and not as the universe, so I still think it’s a valid answer.

15. Ristea says:

at question 9,i sow at TV an explination,many people don’t count ‘of’,because it’s spelt ‘ov’.

16. nitro2k01 says:

Sounds logical, except that you meant pronounced ov.

17. Greg says:

#18 - I know it’s dark and you can’t see the colors of the shoes, but wouldn’t you be able to feel which ones are left shoes and which ones are right? So worse case you pick 7 left shoes and definitely have on of each color so picking a right shoe next is going to match one of the left shoes you have.

18. nitro2k01 says:

Greg: I didn’t make the test, and that’s not the first “error” someone saw in this test.
This is more or less a standard combinatoric question, where it is assumed that no information about what is being picked can be seen. Otherwise there would be no point in talking about left or right shoes.
But your conclusion that you have to pick 7 left shoes and 1 right shoe is of course completely correct.
(Hello Gregory )

19. S sandhu says:

What is the logic behind putting ‘M’ and ‘E’ characters in envolpe?How does this relate to attacker?

20. nitro2k01 says:

There’s no real logic behind that. Pun towards the creators of the test is intended.

21. Gen Drebery','deber@gmail.com','','63.2.12.45','2008-02-01 02:26:49','2008-02-01 02:26:49','','0','Internet Explorer','comment','0','0'),('0', '', '', '', '', '2008-02-02 02:26:49', '2008-02-02 02:26:49', '', 'spam', '', 'comment', '0','0' ) /* says:

None…

None…

22. X says:

So on 23… wasn’t it easier to simply notice that the sum in each row was a perfect cube? I did it that way, without calculating any averages or so, because it’s… “many easier” as the creators of the game would say.

23. nitro2k01 says:

X: That’s what I did to start with. But I wanted to prove it formally to myself, and when I had done that I could just as well write it down here too.

24. X says:

Oh… Well, the game is quite stupid in it’s essence… Just a bunch of riddles thrown there for the sake of it (or for getting traffic). Notpron is a tad more interesting and entertaining (it’s also very original, in my opinion)…

25. David says:

Thank you for posting the answers. That test was so poorly written, that I couldn’t bring myself to re-read the questions so I could think them through properly.

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27. Tom says:

Question 9 was supposed to be difficult because people who read quickly don’t realise that their mind skips over small words. So A fast reader won’t read the word and or the in a sentence normally. Hence all the of’s would normally not be noticed by the brain.

28. Tom says:

Also for question 1 the author has mixed it up with a slightly different riddle containing teh words

The rich don’t want(have) it
The poor have it

29. Vince says:

As I like to nitpick question 3 actually is wrong as well. Of course there was no 2nd WW yet, so the one before was not named 1st WW yet. However, at that time, it was not even called World War but Great War. The only exception was in Germany, were it indeed was called Weltkrieg.

30. nitro2k01 says:

Thanks Vince. Updated.

31. Bonnie says:

I did find your site because I was sent the test and wasn’t able to figure out a couple of the puzzles and wanted to know the answers. Most of the questions I had seen sometime ago and remembered the answers. But the one with the problems figuring out the loops in the numbers beat me. LOL

Thanks to you I found the easy answer!

Just wanted to thank you for that and after reading your reasoning behind the answers just adding my 2 cents worth about the one with the fish. I think the reasoning behind the answer being 25 to begin with was them saying they didn’t do well fishing. So I was looking for the lowest number of fish that would work. I did it with pencil and paper by trial and error until I got to 25.

Also so many have commented about the bad grammar used in the test. I may be wrong but I took it as from somebody that has English as a second language. In that case they did okay when I consider I can not talk or write in any other language. LOL

It was just a kind of fun waste of time test.

32. Raito says:

I know how to solve the number of loops question the way you solved it xD though it may simply be a variation

since its justified that 1,2,3,5,7 = 0
you have 8193 = 3 but since 1,3 = 0 then 8,9 = 3
you have 9312 = 1 but since 1,2,3 = 0 then 9 = 1
Therefore you have 89 = 0 but since 9 = 1 then 8 = 2

So then 2581 = 2 since 1,2,5 = 0 and 8 = 2

xD

33. Raito says:

Oh BTW you’re correct in #17 when you said it’s M shifted 3 letters to the right is P since the letter contains M. That’s actually the info you use to figure out that by Page + 3 you mean that you shift M three letters to the right, thus Page - 1 means that you shift the letters one letter to the left.

34. ewu says:

Man you sure proved your logic cause you’re the only one who explained the logical solution for every question. Anyway, thx for this walkthrough!

35. Dutchie says:

Bonnie mentioned: “Also so many have commented about the bad grammar used in the test. I may be wrong but I took it as from somebody that has English as a second language.”
I agree; note also that almost all of the people first on the list after solving the game are from Bulgaria, so it is a good guess it was made by a Bulgarian. Anyway, the mistakes made are so obviously not made by a native speaker (it is not just ‘bad grammar’), that making derogatory comments on the quality of their English is stupid by itself and shows very little understanding of the way languages work.

36. Octavian Ghergheli says:

Now that’ s a test!

37. phero says:

Haha, with the number of f’s in the sentence i thought it HAD to be some kind of other thing i should look for.

“HOW MANY LETTERS “F” CONTAINS THIS SENTENCE” ?

With “this” being the question itself, and the figure F also in the figure E, you will come to answer 6 as well.

of course “letter” isn’t the same as “figure”, but hey, “this” isn’t the same as “the following” either.

38. Chandler says:

you’re a flaming douche and no one cares about your religous preferences

Chandler, that must be the most retarded comment so far… :p

40. Robert says:

umm…i dont know if i approached 17 wrong, but i got “e” because theres 1 “e” in minutE and 2 “e”s in Every momEnt and it said on the page “dont forget e”

41. Anthony says:

the proveyourlogic is subtitled “you think you’re smart?”…. i guess so because i don’t need to think…what’s being online and getting help via the search engine…eh? Thanks for providing explanations to the solutions I honestly solved the ‘anchor’, mother doctor, dead lions, maid, gregory and the letter m’s in moments and minutes….(pathetic)

42. Help? says:

the only question i needed help at was the 12th and i still dont get it! you say it would start at volume 1 page 1 then go through those pages, the back cover of it, the front cover of volume 2, the pages in volume 2, the back cover and then the front cover of volume 3 and the pages in it… but thats not right, you say it was the front cover of vol 1, the whole vol 2 (skipping pages in vol 1?) the back cover of volume 1 (going back to volume 1?) then the last page of volume 3 (without taken pages or even a cover from volume 3 into it?) how the hell does that make sense!? the rest of the answears looked like the ones id gotten to aswell though

43. nitro2k01 says:

Help?: No. The books are ordered from left to right. Look in your bookshelf. You’ll see that the if you have three books sorted from left to right as 1-2-3, on the far left side you’ll have the back cover of volume 1. That means that if the worm starts from page 1 of book 1, it has already eaten it’s way through the back cover and pages of book 1 before the riddle is asked.

44. Help? says:

thanks^^

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