Question

How many steps are required to break an m x n bar of chocolate into 1 x 1 pieces?

You can break an existing piece of chocolate horizontally or vertically.

You cannot break two or more pieces at once (so no cutting through stacks).

Answer 1

stacks ?

Answer 2

meant rows,eh?

Answer 3

You can't place one piece on top of the other, and break them both with one move.

Answer 4

i like this problem :)

Answer 5

LIKE!

Answer 6

Anyone got an answer for me?

Answer 7

is it ok if i say it? i was kinda hoping someone else would get it.

Answer 8

Doesn't look like anyone else is interested :)

Answer 9

how can people not be interested? its a bar of chocolate!

Answer 10

Maybe they're lactose intolerant?

Answer 11

It might be soya chocolate people!

Answer 12

or like icecream ?

Answer 13

it takes (m times n) times

Answer 14

Incorrect I'm afraid!

Answer 15

lol

Answer 16

mn thats what you need

Answer 17

lol

Answer 18

m n^2

Answer 19

It's close, but it's no cigar.

Answer 20

m are rows right then m^2 n

Answer 21

Your first answer was the closest.

Answer 22

you guys have the right idea for sure. (when saying m*n)

Answer 23

m (n-1) or (m-1)n

Answer 24

Nope, I'm afraid not.

Answer 25

ok let me do this 3x3

Answer 26

we need three column cut

Answer 27

You need 2 columns cut, not 3.

Answer 28

at the bottom

Answer 29

(m-1)+(n-1)

Answer 30

Well 2 cuts to make 3 columns.

Answer 31

yeah sorry 2 thats what i meant

Answer 32

then 3 row cut

Answer 33

@myininaya nope >.<

Answer 34

anyway unless m=n it depend on how you break it. ... good clue ?

Answer 35

wait why

Answer 36

It doesn't depend on how you break it.

Answer 37

As long as all your breaks are straight vertical or horizontal lines.

Answer 38

if we have a 3*2 then we need 2 horizontal cuts and 1 vertical cut
if we have a 4*6 then we need 3 horizontal cuts and 5 vertical cuts

Answer 39

m(n-1) this should be it

(m-1)(n-1)x n

Answer 40

this should be correct

Answer 41

If you have a 3*2, you need 5 breaks. Remember you can only break one piece at a time. You are incorrect Ishaan!

Answer 42

i get 3 breaks how do you get 5?

Answer 43

Once you make your 2 vertical cuts, you have 3 pieces which have to be cut separately. You can't cut all 3 pieces with one cut.

Answer 44

ok

Answer 45

i really dont know im confused

Answer 46

my answer is correct i buy 3x3 bar ( i don't like 2x3 )

Answer 47

I have a hint i want to give but i think it pretty much solves the problem =/

Answer 48

so would we need 60 for a 4*6?

Answer 49

You would need 23 for a 4x6

Answer 50

lol

Answer 51

Think of it like this, if you have an mxn bar, you want to end up with m*n pieces. No matter where you break it the first time, you will end up with 2 pieces afterwards.

I deleted over half of my hint lol

Answer 52

The same can be said of any break. A single break on any piece will create one \(extra\) piece.

Answer 53

m(n-1) + n-1

Answer 54

hows this

Answer 55

i mean

m(n-1) + m-1

Answer 56

LOL

Answer 57

That will work for square pieces only Ishaan, when m and n are equal.

Answer 58

Ah, didn't read your second one

Expand out the brackets.

Answer 59

i say ishaans formula works all the time

Answer 60

no it works for 4x6


m(n-1) + m-1

4(6-1) + 4-1

Answer 61

(m-1)+((n-1)*m) let me see if this works

Answer 62

i got it

Answer 63

myininaya's works too.

Answer 64

Yeah you said "m(n-1) + n-1" first, which I replied to. Your second one is correct, but you can make it simpler.

Answer 65

ahah yeah myininaya works too

Answer 66

yep i tested it on another one

Answer 67

mn -1

Answer 68

m*n-1

Answer 69

(m*n)-1
because you dont have to break the last piece

Answer 70

I expected this question to end way earlier XD

Answer 71

well i got confused

Answer 72

1 break = 2 pieces
2 break = 3 pieces
3 breaks = 4 pieces

? breaks = m*n pieces

Answer 73

it was the understanding of how exactly the bar is being broken that made for confusion.

Answer 74

lol yes

Answer 75

if i hadnt seen the problem before, i dont know how i would have understood it.

Answer 76

ok how about if we did vertical and horizontal cuts without caring about breaking just one at a time?

Answer 77

I guess it would be (m-1)(n-1) then

Answer 78

oh wait i said it ealier
(m-1)+(n-1)

Answer 79

Sorry, put a + sign in there between the brackets.

Answer 80

lol