### Brain Teasers

# Grandmas and Trolls

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

### Answer

2: At each bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.Hide Answer Show Answer

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## Comments

Great teaser! Pretty tough.

I thought it was easy, but fun.

That was good.thanx for the laugh!

Thank you very much mucho gracias

I am pleased to hear that this is a good tesear

ez but fun

ez but fun

SAD!

For being the most popular puzzle in the whole SITE, you get 7, ONLY 7 COMMENTS. GREAT PUZZLE OR TEASER, YEAHH....

For being the most popular puzzle in the whole SITE, you get 7, ONLY 7 COMMENTS. GREAT PUZZLE OR TEASER, YEAHH....

OMG I never knew that thanx for telling me

hm! i couldn't believe i'd got it. i just got it too fast. awesome

Congratz for having the most popular teaser.

I thought this was pretty cute,Good job!

but how do all of you know it's the most popular teaser. Where do you find that information?

but how do all of you know it's the most popular teaser. Where do you find that information?

wow. I GOT ONE right ,,,,,,

sounds familiar..........

anyway a good one! great joke and teaser! lol

anyway a good one! great joke and teaser! lol

sounds familiar..........

anyway a good one! great joke and teaser! lol

anyway a good one! great joke and teaser! lol

Wow, such a simple answer, I was going for 49 cakes lol, real nice teaser though, makes ya think.

i was thinking that it musnt be that simple so i was trying to look for some other answer. lol. fun though

Clever. I thought it was 129 by multiplying by 2 and minusing 1. Great Teaser.

i usually dont like math teasers but this was a good 1

This was too easy

First off, I get such a laugh when I read comments regarding how easy a certain teaser is to that person. Personally, I find it kind of rude. But, that's just my opinion. Secondly, I rate this teaser one of the best and I thought it was written cleverly. Excellent job!

That was cool! I'm not that smart, well I am but i'm kinda ditsy! BUT I GOT IT!!!!!! it was very fun!!!

You know you have a great teasr there!!! I loved reading the story first off..then I started to think and started with a simple number (12) and as I was half way across my first bridge I realized I only needed to be bring 2 cakes! That was very cute!!

I liked it! It was fun. Make me think a little. Good one. Well written

Pretty easy but I liked it.

Very fun teaser. Now, if Grampa wanted his own cake, so you needed three when you got there, how many would you have to start with?

that 1 was really hard, but i liked it, it was well written and... ya!! I got it wrong though

Im not good at math so, it was rather hard. So I thought it was boring but cute.

Amazing job.

+favorite

+favorite

That was really hard, until I realised how easy it was.

To jimrcook - 130 cakes!

To jimrcook - 130 cakes!

OMGosh!! I got it! I loved it but, I got it Yaay! Clever teaser. I am going to have my nine year old work on this one, And I like your name a lot too Gandalf. I have a son named Sam and call him Samwise Gamgee all the time

I must be brain dead today or just not paying attention, that one flew right past me.

Math isn't really my thing

i read it wrong i thought it said you have to give half of cake not half of the cakes you are carring! if i had read it better i would have got it

hey good teaser i got it quick but it was fun!

Very fun!!!!

I worked backwards frfom the last bridge and got it straight away but I was a bit amazed by the answer because it was not what I was expecting. Great puzzle - nice twist!

Ah, recurrence relations! This one was a bit transparent, but still fun. Good job!

Whoa, great teaser!!!

At first I was thinking what kind of calculations I'd have to do to get the answer... then suddenly realized the answer when I thought about starting backwards at the last bridge!

I think this is what makes this teaser so great - the answer isn't what you would expect when you first start reading it!

At first I was thinking what kind of calculations I'd have to do to get the answer... then suddenly realized the answer when I thought about starting backwards at the last bridge!

I think this is what makes this teaser so great - the answer isn't what you would expect when you first start reading it!

I liked this brain teaser because it made me think. I was thinking that there was more cakes then what there really were.

that one was EASY!!!!!

lol. that's kind of a trick teaser...

Great one! I tried to make it much more difficult than it was. But it really made my day when my logical and somewhat math wise husband took my scratch paper and pen and started writing down problems in order to come up with the answer! You fooled him, too! Fabulous!!! He cracked up when he read how simple the answer really is! Keep it up!!!

I think it was too easy. Oh well, you did better than me, i haven't been able to come up with that many teasers so i give you props. it's hard to come up with a teaser thats not too easy or too hard!

nice 1...

i took the bait and tried to calculate the answer

then i knew it was 2

good stumper

i took the bait and tried to calculate the answer

then i knew it was 2

good stumper

Now this was a good brain teaser.

My sister gave this interesting alternative. Assume the trolls in the past were NOT nice trolls, so they now have a bunch of cakes. In that case, if you start with one cake, you give the troll a half a cake, and the troll (now nice) takes a whole one from the stock pile previously amassed and gives it to you. You now have 1.5 cakes. I find it very interesting that after seven bridges, you will have (mathematically) within 1% of two cakes to give to gramma. Since cakes surely vary by more than that anyway, this would surely satisfy gramma on her birthday, and would be a great birthday story to boot.

Mar 24, 2005

that was so smart!!

Thanks for the teaser! Gracias ! Soy contenta... Great one..

Thanks for the teaser! Gracias ! Soy contenta... Great one..

Um praisemusictlp the point is that there are trolls waiting to take have your booty and if you have more than 2 cakes than it would be a lot harder. Thanx for the comments.

quite easy but fun

Man, I want some cake now.

this was fun and easy, and it could have easily thrown people off

cake.... did sum1 say sumthin about cake?....i luv cake!!!!

Praise and Akg:

Do either of you have anything of your own that is better.

Good teaser.

Do either of you have anything of your own that is better.

Good teaser.

HeHee now that's what i call a piece of cake Lovely job, goes staraight to my faves

I thorougly enjoyed that one. I tried to work backwards from the house, but with no avail, so I looked at the answer. follower by a slap to my forehead *doh*

simple when you know the answer - but fun

simple when you know the answer - but fun

Good job. For some reason I got this one right away. Must be early enough in the morning that my brain is still relaxed

I was thinking along the same lines as jimrcook's solution. Except you could start with no cakes at all, so at the 1st bridge you give 0 and take 1 cake. continue to 7th bridge and you can go back and forth across the 7th bridge until you cake total reaches infinitely close to 2 cakes such that grandma can't tell the difference.

Just realised the my above solution is wrong in that:

1. the cakes will not be made you, and you want to give grandma cakes you've made.

2. question requires EXACTLY 2 cakes, above solution only gives 1.999999..... cakes.

^^

1. the cakes will not be made you, and you want to give grandma cakes you've made.

2. question requires EXACTLY 2 cakes, above solution only gives 1.999999..... cakes.

^^

Praise and Akg:

Before you try to vent in the comments page teasers, please take note that the teasers here has been well thought of before submissions. Also, before saying anything derogatory, I don't see you trying your best at all by submitting a teaser .

Before you try to vent in the comments page teasers, please take note that the teasers here has been well thought of before submissions. Also, before saying anything derogatory, I don't see you trying your best at all by submitting a teaser .

Gandalf, nice teaser btw Keep it up.

AWESOME, cute teaser! Like the fantasy aspect! Great job and keep 'em coming!

A little easy for my taste

Mar 19, 2006

This is actually a very good one.

Mathematically speaking you can also start with 4/7 (0.5714) cakes and get to 2 cakes by 7-th bridge. This is more economical but the pressure is on the first troll to give you 1 cake even though you gave him less than one

Mathematically speaking you can also start with 4/7 (0.5714) cakes and get to 2 cakes by 7-th bridge. This is more economical but the pressure is on the first troll to give you 1 cake even though you gave him less than one

I DON'T KNOW WHO'S SPEAKING FOR MATHMAMETICS, BUT THE ONLY WAY TO GET TO GRANDMA'S WITH "EXACTLY" TWO CAKES, IS TO START WITH TWO CAKES, NOT 4/7!!!

ANY NUMBER LESS THAN 2 WILL NOT GET YOU TWO CAKES, CLOSE, BUT NO CIGAR.

ANY NUMBER LESS THAN 2 WILL NOT GET YOU TWO CAKES, CLOSE, BUT NO CIGAR.

Well I went all mathematical and wrote down a formula -

x-7(0.5x)+7 = 2

where x is what you started with. By now I should have known the answer, but still my superactive brain (as it gets sometimes) actually solved this bit by bit and arrived at the shocking answer:2!

Still laughing!

x-7(0.5x)+7 = 2

where x is what you started with. By now I should have known the answer, but still my superactive brain (as it gets sometimes) actually solved this bit by bit and arrived at the shocking answer:2!

Still laughing!

A good thinker on the sweeter side. Good work.

Very nice an funy

I started out also trying to write a formula, but realized that you can't just multiply by 7 because the amount changes each time before it's halved, so instead of doing the operations on x seven times you have to do the operation on x once, then do the operation on that amount, and so on.

I LOVE this one!!! This is classic, it's what I think of when I think of a teaser, because it gets you thinking and calculating, and then because of one of those magical properties of numbers the answer is simple!

I also got it, YAY!, by stopping the scribbling and starting at the end, with two, and realized, Voila! Eureka! That eureka feeling is what I really LOVE about A GOOD TEASER! Thanks so much! I sent it to some friends and family!

I LOVE this one!!! This is classic, it's what I think of when I think of a teaser, because it gets you thinking and calculating, and then because of one of those magical properties of numbers the answer is simple!

I also got it, YAY!, by stopping the scribbling and starting at the end, with two, and realized, Voila! Eureka! That eureka feeling is what I really LOVE about A GOOD TEASER! Thanks so much! I sent it to some friends and family!

I got it! Yeah!!

Ifelt sorry for the trolls they are going hungry no cakes BUMMER

So are the trolls stupid? I mean they dont get nothing why are they there if every one in make believe figure this out they just take two of everything and never really pay for crossing they bridges. LOL.

But seriously. really fun teaser you got me writing all this numbers cus I wanted to leave the trolls with at least on cake. But the answer came to after I finished reading the teaser. GOOD WORK MAN!!

But seriously. really fun teaser you got me writing all this numbers cus I wanted to leave the trolls with at least on cake. But the answer came to after I finished reading the teaser. GOOD WORK MAN!!

very good one keep 'em coming!

Nice teaser. Poor trolls should brush up on their math, if they want to have some cake! Those who start with 2 cakes sort of eat the cake and have it too!

Good teaser!!! It took me a little bit to figure out how she would have two... before i realized the troll gave one back. Oh well, wonderful teaser!

I just worked it backwards, therefore it was easy.

I thought it was easy until I saw the calculator and then I thought it must be hard. YOU GOT ME. Nice! I hate/love that.

That was the best one yet. I love hard/easy brain teasers.

PS you got me

PS you got me

That really made my brain think... for a second anyway, then I had to cheat and look at the answer.

This was cute, but so easy, I can hardly consider it a brain teaser.

No challenge. It needs more numbers that don't pertain to the puzzle to make it more confusing.

No challenge. It needs more numbers that don't pertain to the puzzle to make it more confusing.

WWWOOOOOHOOOO!!! I got this one without the calculator!!! I liked it!!!!

I thought this was hard... and then I realized the reason why I kept getting the wrong answer was because I had forgotten the part about getting one cake back from each troll! Yeah I feel ditzy now, cuz the answer is so obvious (and here I was, trying it with 1,000) but it was a really good teaser! thanks!

Hey doing good .thought this one was pretty easy but it was something to put my time on.

Thanks for the challenge

Thanks for the challenge

Great teaser! Ugh it didn't occur to me that working backwards would work so I started with numbers like 200 and 180 and stuff. After that didn't work, I worked backwards and I got it. I really liked the teaser! It's going on my favorites list!!

Maybe including a calculator was what threw many us off. Like brainster and shawneeo, I decided do it without your calculator, so I got out paper (like a good algebra student) and tried to create an equation ... the whole bit. Argghhh! You got a BUNCH of us! Thanks for the FUN! It is a FAVE, for sure.

I was thinking half of one of the cakes, not half of the cakes. WOW!!

Hehe, that was pretty simple, I just started of by working backwards. Great job, kudos for such a great teaser, I loved it. Simple, fun, and I can see how it can be tough for some.

Lol, took me back to my childhood. Haven't seen this one in decades. Thanks for the childhood memories.

this 1 is kinda old but its a good 1. ive seen it everywhere tho.

i was going like half of 7 is... so i was way off i was being really stupid ;bad day

I just like guessed two....wow....lucky guess I guess... :-p

Neat - should really be in the 'trick' category.

that was waaaaaaay to easy!!!!

I Like. Pretty Easy,

but Lots Of Fun.

but Lots Of Fun.

It would have been better if it was parfaits instead of cakes. Everybody loves parfaits. If anyone says lets have a parfait you never hear someone say no I don't like parfait. Mmmm parfait, well it was close anyway,

I loved this teaser. I sat down to do it and I thought, this is really hard. How do I do this? So I started from the bottom, with two cakes, and soon realized the answer was 2. But I thought, it surely couldn't be that easy so I used a bunch of numbers and divided by 2 and added one, but I kept getting fractions. So then I realized that it must be 2 and how thrilled I was to find that I was right! Thanks for a really great teaser.

Being a Grandma and loving trolls I feel really dumb letting this one go over my head. I usually try to tackle a problem head on so I suppose that's why I didn't try to go backward. Nice teaser tho.

i still love you vlerma

what about about when it's time to go home? Whatcha gonna do then? 7 more bridges to cross. Do the trolls become angry and eat half of you? LOL

too easy and ridiculous.

Good puzzle.

I started thinking in binary: the last digit must be zero before visiting each troll, and each troll increments the number by one. Using this I got 10000010 in binary, which is 130 in decimal.

Hence, there are 2 solutions.

I started thinking in binary: the last digit must be zero before visiting each troll, and each troll increments the number by one. Using this I got 10000010 in binary, which is 130 in decimal.

Hence, there are 2 solutions.

I've just found out that 130 is wrong

There will remain 4 cakes, not 2.

There will remain 4 cakes, not 2.

Nov 11, 2006

x(n+1) = x(n)/2 + 1;

=> x(n) = 2( x(n+1) - 1 )

x7 = 2; => x6 = 2(2-1) = 2;

x6 = 2; => x5 = 2(2-1) = 2;

x5 = 2; => x4 = 2(2-1) = 2;

..

..

x2 = 2; => x1 = 2(2-1) = 2;

Nice question;

=> x(n) = 2( x(n+1) - 1 )

x7 = 2; => x6 = 2(2-1) = 2;

x6 = 2; => x5 = 2(2-1) = 2;

x5 = 2; => x4 = 2(2-1) = 2;

..

..

x2 = 2; => x1 = 2(2-1) = 2;

Nice question;

A little easy, but very enjoyable.

luv it!

Excellent!

Ooh, venkataramanam is getting out the series formulae...

Very good teaser. Pretty easy with a few seconds thought, but nice and fun!

Good job!

Very good teaser. Pretty easy with a few seconds thought, but nice and fun!

Good job!

Easy, but fun. Heh, at first I was wondering if I'd have to start splitting them up into half-cakes.

I thought more than I should have.

I was pleasantly pleased when I saw the answer. Haha!!

I was pleasantly pleased when I saw the answer. Haha!!

yawn

how ez was this??? piece of cake........ lol sweeeeet....

but i like the real brain drainers where u have to think long and hard without any tricks---- but still... thgs was a good one.....

but i like the real brain drainers where u have to think long and hard without any tricks---- but still... thgs was a good one.....

That was really funny

I didn't remember this from last year, but i got it (again.)

Got it right away, great teaser

Another brilliant teaser! Although a little bit on the easy side! It does get the brain in gear. Keep up the fantastic work!

I loved it! Clever and tricky even for many veterans. It doesn't get any better than that for most of the crowd. Good job!

I thought it was great! Thanks

Bah! You should have made it 1729 bridges and "Trick" category!

seems like there are several answers, at any bridge you can get to 2, and from then on it stays 2

I can solve some of the puzzles on this site, but I can not figure this one.

I thought this one was well written and I GOT IT. It was a lot of fun.

Easy & fun! I kept at it, thinking there had to be a more difficult solution!

I don't get the answer!! How many cakes would you have to leave with?

I started with the thought that you had to end up at Grama's house with 2 cakes . Therefore the 7th troll had to give you 1 cake to add to your 1 cake and the rest was easy. So easy that I got out the paper, pencil, and calculator before I realized it wasn't hard at all. But I can see how it could confuse some people into thinking it was a big math problem. It should be called a trick. But whatever it is , I loved it.

how is the answer two?

I'd have gotten that one if I hadn't been so lazy.

A good puzzle. You can either get bogged down quickly with complicated maths and get the wrong answer or think laterally and get the correct answer quite quickly. Luckily my lateral thinking muscle woke up for just long enough otherwise I'd still be on it now!

Well done. Nice storyline and good fun.

Well done. Nice storyline and good fun.

That really tricked me. I didn't try to figure it out though, since I knew that with every other even number, if you divide it in two then add one you will get an odd, which would divide into somthing and 1/2. Didnt think of the only exception...

Cool brainteaser, makes you use your noodle!

I got it!

Very interesting teaser~

Very interesting teaser~

Oneheartbroken: think of it this way....you leave with 2 cakes. At the first bridge, give one to the first troll. Now you have 1 and he has 1. He's going to be nice and give you one back. Now you have 2 again. On to the next bridge and it all repeats until you get to Grandma's!

almost tried to figure it all out, but started going backwards from the last bridge and realized the answer. potentially tricky though. nice.

Good one And the comments, as always, are entertaining, frustrating, funny, and enjoyable!

I loved this Made me smile

*Adds to faves*

*Adds to faves*

Very fun, and very easy. Thanks

I did 2 to the 7th power, then added 7..... gave me 263 cakes!!!!!

But if I was a troll, then I would want a cake, and I would realize that taking 1/2 from 2 and giving one back would leave me with nothing, and I would be angry.

But if I was a troll, then I would want a cake, and I would realize that taking 1/2 from 2 and giving one back would leave me with nothing, and I would be angry.

But if the troll takes one cake and then gives one back, why does he bother?

That was easy, but fun. You would think that the trolls would want to keep some of cupcakes for themselves, but they are not very smart in this story.

2 is the obvious answer which of course I answered but when you work out the problem for any number from 0-100 you get pretty darn close to 2 anyway so the smart thing to do would be to take 3 so you can always have a portion to taste for yourself.

I love it! The smartest one I ever heard! Putting it on my favorites list!

Wow, that was neat. I'm so glad I thought to start from the end!

To anyone wondering why the trolls even bother taking a cake then giving it back: trolls don't like cake! They just like scaring people!! And until they gave that cake back, you were SCARED, WEREN'T YOU!? Muhaha.

To anyone wondering why the trolls even bother taking a cake then giving it back: trolls don't like cake! They just like scaring people!! And until they gave that cake back, you were SCARED, WEREN'T YOU!? Muhaha.

Good answer, Qrystal!

great teaser!

love it

tricky but fun!

love it

tricky but fun!

Very interesting.

Great teaser. I loved it.

my math teacher told us that one once

Nice question, but I've seen a couple of people giving incorrect or complex formulas. Here's the algebra that gives the solution:

( ( ( ( ( ( ( ( ( ( ( (x/2+1) /2)+1) /2) +1) /2) +1) /2) +1) /2) +1) /2) +1 = 2.

After doing the first 2 operations, the simple solution shows itself without having to complete the whole sequence, but it's nice if you want to solve for a different amount of cakes .

( ( ( ( ( ( ( ( ( ( ( (x/2+1) /2)+1) /2) +1) /2) +1) /2) +1) /2) +1) /2) +1 = 2.

After doing the first 2 operations, the simple solution shows itself without having to complete the whole sequence, but it's nice if you want to solve for a different amount of cakes .

That is wrong... if you bring two cakes, you give half of one each time. That means you have 1.5 afterwards, then 2.5?!

Read it again uhhhh,

"you have to give them half of the cakes you are carrying" not half of a cake.

"you have to give them half of the cakes you are carrying" not half of a cake.

lol why some peope think it's 130? its two: >2< !!! because everytime you're giving 2/2=1, and they give you this 1 back! so, number of the cakes doesn't change!

I loved this one. When working with math, you have to start with the known. We know we want 2 at the end, and at each bridge we leave with (x/2) + 1 cake.

So after the last bridge we want (x/2) + 1 = 2

x/2 = 1

x = 2

So the only way to have 2 cakes for grandma is to have 2 cakes before the last bridge! Since we need 2 cakes before the last bridge, we see that it doesn't matter how many bridges there are, if we have 2 going in, we have 2 going out, thus the answer is 2.

Great puzzle!

So after the last bridge we want (x/2) + 1 = 2

x/2 = 1

x = 2

So the only way to have 2 cakes for grandma is to have 2 cakes before the last bridge! Since we need 2 cakes before the last bridge, we see that it doesn't matter how many bridges there are, if we have 2 going in, we have 2 going out, thus the answer is 2.

Great puzzle!

I did not get it, until I re-read it. Tricky.

I got 310

Now that's what I call mental statistics! I like it!!!

Another way was to put the cakes in your wagon and carry a gun. Shoot the troll before you cross the bridge.

Fun!

Enjoyed this one again. Great teaser.

We got this teaser for a school problem. We solved it in like two seconds, but it's still a fun teaser.

Don't like math so did not try!

Loved this one! I remember doehead from years ago. I wonder what happened to him/her.

This one was fun.

I missed the part where it said you got a cake back so I did the math and came up with a large number. I knew this could not be right so reread the question (correctly this time) *FACEPALM* Duh! Don't even need math to figure it out!

lol @Doehead - that would work too.. But hope you are only using a tranq gun. No need to kill the kindly trolls.

I miss reading his comments too Gayle

lol @Doehead - that would work too.. But hope you are only using a tranq gun. No need to kill the kindly trolls.

I miss reading his comments too Gayle

Actually very simple math. I heard that DOEHEAD bought a new convertible and drove off into the sunset. I miss him too.

I loved it! One of the few math ones I got. I started working backwards and I'm like, okay, so after the 6th I have two...wait, wouldn't that work for every one? Great teaser. Could also go in the trick category, although it's not really a trick. Just misleading.

Fun and easy

i did not get it for 3 tries but after i read some comments it was 2 cakes >.< HOW DID I GET THAT SO WRONG DX

Gosh, I actually managed to not get this one. Usually, I would set up a set of equations. If I had used this method, I would probably have figured out the trick tricked. However, I got lazy and used the faster method of reversing everything, but unfortunately, I ended up adding instead of subtracting one each time, ending up with 510 cakes.

I came up will a formula

U= ((n-2)/(2^b))+2

b is the total number of bridges, n is the number of cakes you take to start off with and U is the number of cakes the granny receives

It looks like as the number of bridges (b) tends to infinity no matter what number of cakes the girls takes with her (n) the granny will always receive 2. Even if the girl didn't take any cakes the granny would still get two cakes if there were an infinite number of bridges which is strange. Please correct me if I'm wrong

U= ((n-2)/(2^b))+2

b is the total number of bridges, n is the number of cakes you take to start off with and U is the number of cakes the granny receives

It looks like as the number of bridges (b) tends to infinity no matter what number of cakes the girls takes with her (n) the granny will always receive 2. Even if the girl didn't take any cakes the granny would still get two cakes if there were an infinite number of bridges which is strange. Please correct me if I'm wrong

how do you answer i know it but i dont know how to answer

excellent!!!!

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