21 replies to this topic

[bonanova]

You unwrap a giant Hershey bar. The type that is scored, so that it can be broken into smaller pieces. You note the bar has exactly m squares along its length and n squares along its width.

You wish to break the bar up into all small squares. How many breaks are required? Stacking is not allowed, and the breaks are always made along a straight line.

[hhh3]

hmm... there are 42 views and no answer... then i guess i missed the whole complexity of the Q somwer... here's a soln thats more like a

Spoiler for stab in the dark

(m-1)*(n-1)

[jordge]

Spoiler for No math involved

Every break increases the number of pieces by one by taking a larger piece and turning it into two smaller pieces. You start out with one large piece and continue breaking until all pieces are as small as allowed. If the total number of small pieces is n*m then the number of breaks to get that many is always (n*m)-1.

[Rob_Gandy]

Spoiler for I would say

(n-1)+(m-1) or n+m-2. It says you can't stack them, but it doesn't say that you can't hold the bar together as if it wasn't broken.

[joef1000]

Spoiler for definitely

mn-1
It is in my 'Professor Layton and the mysterious village' game.

[Emil]

Hi all, this is my first try...ever:

Is this a possible answer?:

(n-1) + (m-1)*n

[nakulendu]

Spoiler for Choco Breakup

mn-1. You can have it either a. Breaking the m rows first (m-1 breaks) and then breaking each of the m sticks into n pieces (total of m(n-1). In all mn-1 b. Breaking the n columns first (n-1 breaks) and then breaking each of the n sticks into m pieces (total of n(m-1). In all mn-1

[jordge]

Spoiler for small errors

Spoiler for Choco Breakup

mn-1. You can have it either a. Breaking the m rows first (m-1 breaks) and then breaking each of the m sticks into n pieces (total of m(n-1). In all mn-1 b. Breaking the n columns first (n-1 breaks) and then breaking each of the n sticks into m pieces (total of n(m-1). In all mn-1

There are actually more ways to break it up, not just do all m and then do all n. You could pick up any joined piece and break it in any order. But looking at your example for m first:
Break all the m rows: (m-1) breaks
Break all the m sticks into n pieces: m(n-1) breaks or (mn-m) breaks
Add all the breaks: (m-1) + (mn-m) = mn-1

[Prof. Templeton]

Stacking is not allowed, and the breaks are always made along a straight line.

Only stacking in a third dimension is not allowed? Cut pieces may be moved around on the plane or rotated to be cut further?

What about flipping of pieces? (although I fail to see how that may be advantageous at this point)

[curr3nt]

Are we allowed to warp the fabric of space and time?