Braingle Lite



Grandmas and Trolls

Category:Math
Submitted By:Gandalf
Fun:**** (3.22)
Difficulty:** (1.38)



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?

Show Answer



Comments on this teaser


Posted by rydell02/18/05
Great teaser! Pretty tough.

Posted by castanz02/18/05
I thought it was easy, but fun.

Posted by Goth_Goddess66602/18/05
That was good.thanx for the laugh! :lol:

Posted by Gandalf02/19/05
Thank you very much mucho gracias :D

Posted by Gandalf02/21/05
I am pleased to hear that this is a good tesear

Posted by dalt8802/27/05
ez but fun

Posted by dalt8802/27/05
ez but fun

Posted by DummyisDumb03/01/05
SAD! For being the most popular puzzle in the whole SITE, you get 7, ONLY 7 COMMENTS. :D :) GREAT PUZZLE OR TEASER, YEAHH....

Posted by Gandalf03/01/05
OMG I never knew that thanx for telling me

Posted by iconofsin03/04/05
Congratz for having the most popular teaser. :D :D

Posted by ZOE563903/04/05
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?

Posted by y4n403/15/05
sounds familiar.......... anyway a good one! great joke and teaser! lol :lol: :D :wink:

Posted by y4n403/15/05
sounds familiar.......... anyway a good one! great joke and teaser! lol :lol: :D :wink:

Posted by r3lish03/18/05
:lol: i was thinking that it musnt be that simple so i was trying to look for some other answer. lol. fun though

Posted by Master_Yoda03/18/05
Clever. :D I thought it was 129 by multiplying by 2 and minusing 1. Great Teaser. :)

Posted by krabcat03/19/05
i usually dont like math teasers but this was a good 1

Posted by cookeechick0503/19/05
This was too easy 8) :roll:

Posted by Riki03/19/05
First off, I get such a laugh when I read comments regarding how easy a certain teaser is to that person. :lol: 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! :D

Posted by madgurl3103/19/05
That was cool! I'm not that smart, well I am but i'm kinda ditsy! BUT I GOT IT!!!!!! it was very fun!!! :D 8)

Posted by CHUCKLZ03/19/05
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! :lol: That was very cute!!

Posted by Kal2203/19/05
I liked it! It was fun. Make me think a little. Good one. Well written :lol:

Posted by Kinergy03/19/05
Pretty easy but I liked it.

Posted by jimrcook03/19/05
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? :wink:

Posted by Brenna03/19/05
that 1 was really hard, but i liked it, it was well written and... ya!! I got it wrong though :oops: :) 8)

Posted by thetrumonk03/19/05
Im not good at math so, it was rather hard. So I thought it was boring but cute. :D

Posted by tissue03/19/05
Amazing job. +favorite

Posted by Dave03/19/05
That was really hard, until I realised how easy it was. To jimrcook - 130 cakes!

Posted by tamjp03/19/05
:o OMGosh!! I got it! :D I loved it but, I got it :wink: 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 :wink:

Posted by mr_brainiac03/19/05
I must be brain dead today or just not paying attention, that one flew right past me. :-?

Posted by j_mon03/19/05
Math isn't really my thing :-?

Posted by PBlover03/19/05
Very fun!!!! :D :lol:

Posted by Jimbo03/19/05
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! :D

Posted by nardhelain03/20/05
Ah, recurrence relations! This one was a bit transparent, but still fun. Good job!

Posted by ultimatehorse03/20/05
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! :D

Posted by Jessa03/20/05
I liked this brain teaser because it made me think. I was thinking that there was more cakes then what there really were. :P

Posted by brain_dead03/20/05
that one was EASY!!!!! :D

Posted by DummyisDumb03/20/05
lol. that's kind of a trick teaser...

Posted by froggygg03/20/05
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!!! :lol: :lol: :lol: :lol: :lol:

Posted by Sarah522576603/20/05
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! :P

Posted by timilee03/20/05
nice 1... i took the bait and tried to calculate the answer :-? then i knew it was 2 :oops: good stumper

Posted by MEJOHN03/21/05
Now this was a good brain teaser. :P

Posted by jimrcook03/23/05
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.

Posted by Carmenio03/26/05
Thanks for the teaser! Gracias ! Soy contenta... Great one..

Posted by Carmenio03/26/05
Thanks for the teaser! Gracias ! Soy contenta... Great one..

Posted by Gandalf03/30/05
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.

Posted by moktapa04/23/05
quite easy but fun

Posted by darthforman05/21/05
Man, I want some cake now. :lol:

Posted by ane9259005/29/05
this was fun and easy, and it could have easily thrown people off :D

Posted by zigthepig07/03/05
cake.... did sum1 say sumthin about cake?....i luv cake!!!! :lol: :lol: :D :D

Posted by Swordoffury139207/26/05
Praise and Akg: Do either of you have anything of your own that is better. Good teaser. :)

Posted by smarty_blondy08/24/05
HeHee now that's what i call a piece of cake :lol: Lovely job, goes staraight to my faves :wink:

Posted by dutchymonster09/07/05
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 :D

Posted by AZTTT09/16/05
Good job. For some reason I got this one right away. Must be early enough in the morning that my brain is still relaxed :lol:

Posted by Laboomsikashod09/19/05
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.

Posted by Laboomsikashod09/19/05
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. ^^

Posted by Nytwynd10/10/05
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 :roll:.

Posted by Nytwynd10/10/05
Gandalf, nice teaser btw :) Keep it up.

Posted by teen_wiz02/09/06
AWESOME, cute teaser! Like the fantasy aspect! Great job and keep 'em coming! :D :D :D 8)

Posted by keveffect102/17/06
A little easy for my taste :-?

Posted by lmurray03/19/06
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.

Posted by brainster03/19/06
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! :lol:

Posted by OldChinaHand03/19/06
A good thinker on the sweeter side. Good work. 8)

Posted by IvoM03/19/06
Very nice an funy

Posted by shawneeo03/19/06
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! :D

Posted by bradon18200103/19/06
I got it! Yeah!! :D

Posted by bobbet03/19/06
Ifelt sorry for the trolls they are going hungry no cakes BUMMER :D

Posted by Jokawolf03/19/06
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. :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!!

Posted by buddirose03/19/06
very good one keep 'em coming! :D :P :) :lol:

Posted by RRAMMOHAN03/19/06
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! :lol: :lol: :lol: :lol:

Posted by EVOLNI03/19/06
Good teaser!!! It took me a little bit to figure out how she would have two... before i realized the troll gave one back. :oops: Oh well, wonderful teaser!

Posted by JessicaLynn03/19/06
I just worked it backwards, therefore it was easy. :D

Posted by thimblenoggin03/19/06
:D 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. :D

Posted by Budrageous03/19/06
That was the best one yet. I love hard/easy brain teasers. PS you got me

Posted by kashby03/19/06
That really made my brain think... for a second anyway, then I had to cheat and look at the answer. 8) :o :-?

Posted by kacsing03/19/06
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.

Posted by KatV03/19/06
WWWOOOOOHOOOO!!! I got this one without the calculator!!! I liked it!!!! :D :lol: :D :lol: :D :lol:

Posted by ginny32203/19/06
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! :D 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!

Posted by 2hip4you03/19/06
Hey doing good :wink: .thought this one was pretty easy but it was something to put my time on. Thanks for the challenge

Posted by lindquist_2503/19/06
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!! :D :P :) 8) :wink: :lol:

Posted by iteachkids03/19/06
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. :o :o :o Argghhh! You got a BUNCH of us! Thanks for the FUN! It is a FAVE, for sure. :D

Posted by wizkid03/19/06
I was thinking half of one of the cakes, not half of the cakes. WOW!! :lol:

Posted by WyndRyder7603/19/06
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.

Posted by guthing03/19/06
Lol, took me back to my childhood. Haven't seen this one in decades. Thanks for the childhood memories. :D

Posted by amygurl10103/19/06
this 1 is kinda old but its a good 1. ive seen it everywhere tho. :roll:

Posted by cartwheel_queen03/19/06
i was going like half of 7 is... so i was way off i was being really stupid :-? ;bad day :evil:

Posted by tintiniscool03/19/06
I just like guessed two....wow....lucky guess I guess... :-p

Posted by wizofaus03/19/06
Neat - should really be in the 'trick' category.

Posted by hockeygirl03/19/06
that was waaaaaaay to easy!!!! :evil:

Posted by bluehawk03/19/06
:lol: I Like. Pretty Easy, but Lots Of Fun. :lol: :wink: 8)

Posted by ggssking03/19/06
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,

Posted by mysweetjolie03/20/06
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. :)

Posted by vlerma03/20/06
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. :oops:

Posted by Vigo9503/20/06
i still love you vlerma :D

Posted by djmac7103/20/06
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 :evil: :evil: :evil: :evil: :evil: :evil: :evil: :o :( :o

Posted by nurpin03/26/06
too easy and ridiculous.

Posted by ulan08/30/06
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. :wink:

Posted by ulan08/30/06
I've just found out that 130 is wrong :oops: There will remain 4 cakes, not 2.

Posted by teasermaster12/19/06
A little easy, but very enjoyable.

Posted by sugarnspice4u702/17/07
luv it! :lol:

Posted by cloughme03/19/07
Excellent! :wink:

Posted by Smudge03/19/07
Ooh, venkataramanam is getting out the series formulae... Very good teaser. Pretty easy with a few seconds thought, but nice and fun! Good job!

Posted by AbsurdHero03/19/07
Easy, but fun. Heh, at first I was wondering if I'd have to start splitting them up into half-cakes.

Posted by katjojo03/19/07
I thought more than I should have. I was pleasantly pleased when I saw the answer. Haha!! :lol: :lol:

Posted by puttumup03/19/07
:o yawn :o

Posted by kitty72803/19/07
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..... 8) :wink: :lol:

Posted by sftball_rocks1303/19/07
That was really funny :lol:

Posted by bradon18200103/19/07
I didn't remember this from last year, but i got it (again.) :o

Posted by Mon0503/19/07
Got it right away, great teaser :lol:

Posted by Pizzazz2u03/19/07
Another brilliant teaser! Although a little bit on the easy side! :wink: It does get the brain in gear. :P Keep up the fantastic work! 8) :wink:

Posted by rambo6703/19/07
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! :wink:

Posted by cassiemark03/19/07
I thought it was great! Thanks :)

Posted by FatHead03/19/07
Bah! You should have made it 1729 bridges and "Trick" category! :lol:

Posted by fishfrank03/19/07
seems like there are several answers, at any bridge you can get to 2, and from then on it stays 2

Posted by feste03/19/07
I can solve some of the puzzles on this site, but I can not figure this one.

Posted by phyllisa03/19/07
I thought this one was well written and I GOT IT. It was a lot of fun. :D

Posted by RoknRobn22803/19/07
Easy & fun! I kept at it, thinking there had to be a more difficult solution! :lol:

Posted by oneheartbroken03/19/07
I don't get the answer!! How many cakes would you have to leave with? :-? :roll: :oops: :wink: :( :cry: :o :x

Posted by auntiesis03/19/07
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. :lol: :D :) :P 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. :P

Posted by oneheartbroken03/19/07
how is the answer two? :-? :roll: :oops: :wink: :( :cry: :o

Posted by mrtickles03/19/07
I'd have gotten that one if I hadn't been so lazy.

Posted by lezh03/19/07
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.

Posted by frozenrose_88503/19/07
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...

Posted by parayik03/19/07
Cool brainteaser, makes you use your noodle! :lol:

Posted by ViaTunisi03/19/07
I got it! Very interesting teaser~ :)

Posted by breathesunshine03/19/07
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!

Posted by Shikamaru03/19/07
almost tried to figure it all out, but started going backwards from the last bridge and realized the answer. potentially tricky though. nice. :-? :D :P :roll: :wink: 8) :lol:

Posted by jabdr03/19/07
Good one :lol: And the comments, as always, are entertaining, frustrating, funny, and enjoyable! :roll:

Posted by sftball_rocks1303/19/07
I loved this :D Made me smile :lol: :D*Adds to faves* :D

Posted by kman61303/19/07
Very fun, and very easy. Thanks

Posted by GobyDude03/19/07
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.

Posted by jcann03/19/07
But if the troll takes one cake and then gives one back, why does he bother?

Posted by asfidelino03/19/07
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. :D :D :lol: :lol:

Posted by jacstop03/20/07
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.

Posted by notsosmart11103/20/07
I love it! The smartest one I ever heard! Putting it on my favorites list!

Posted by Qrystal03/21/07
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.

Posted by jcann03/21/07
Good answer, Qrystal! :D

Posted by measle102503/24/07
great teaser! love it tricky but fun!

Posted by jamy40003/25/07
Very interesting.

Posted by lukeschett04/14/07
Great teaser. I loved it.

Posted by javlad2708/15/07
my math teacher told us that one once

Posted by Spockinasmock12/30/07
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 .

Posted by uhhhh01/13/08
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?!

Posted by Spockinasmock01/18/08
Read it again uhhhh, "you have to give them half of the cakes you are carrying" not half of a cake.

Posted by bubeshka1301/11/09
lol why some peope think it's 130? :D 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!

Posted by Paladin03/13/09
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!

Posted by drussel304/19/09
I did not get it, until I re-read it. Tricky.

Posted by gargph03/19/10
I got 310 :o

Posted by science12nerd03/19/10
Now that's what I call mental statistics! :D I like it!!!

Posted by doehead03/19/10
Another way was to put the cakes in your wagon and carry a gun. Shoot the troll before you cross the bridge. :lol: :lol: :lol:

Posted by patiencewithaP03/19/10
Fun! :D

Posted by auntiesis03/19/10
Enjoyed this one again. Great teaser. :D :D :D

Posted by LemurHotel11/11/10
We got this teaser for a school problem. We solved it in like two seconds, but it's still a fun teaser. :D

Posted by Babe03/19/13
Don't like math so did not try! :(

Posted by gaylewolf03/19/13
Loved this one! I remember doehead from years ago. I wonder what happened to him/her. :wink: :)

Posted by jaycr03/19/13
This one was fun.

Posted by HABS293303/19/13
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

Posted by cutebug03/19/13
Actually very simple math. :D :D I heard that DOEHEAD bought a new convertible and drove off into the sunset. :wink: :wink: I miss him too.

Posted by kitty-cat03/19/13
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? :D Great teaser. Could also go in the trick category, although it's not really a trick. Just misleading. :P

Posted by Haagenti03/19/13
Fun and easy :)

Posted by catsrule774904/20/13
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 :o

Posted by JQPublic08/30/13
Gosh, I actually managed to not get this one. :oops: 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. :oops: :oops:




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