How many pieces can a donut be cut into?

How many pieces can a donut be cut into?

If you can move the pieces, then the simplest solution is 2^6 = 64 pieces. Simply halve the pieces with each cut successively 6 times. Each cut will double the number of pieces. You can either stack the pieces on top of one another or line them up horizontally before you cut.

Can you divide a cake into 8 pieces with 3 cuts?

Step 1: Cut the cake into quarters (4 pieces) using 2 of the cuts – one horizontally down the centre of the cake and the other vertically down the centre of the cake. Step 3: Finally, you can just cut that stack of 4 pieces in half – using your third and final cut – and then you will end up with 8 pieces of cake!

How do you cut a donut into 6 pieces with 2 cuts?

You can also get 6 pieces by rearranging between the cuts. Put the donut flat on the table and make a downwards cut through the center. That gives you two C shapes. Align one on top of the other and make another downward cut, slicing off the ‘prongs’.

How do you cut a donut into 12 pieces with only 3 cuts?

You stack these one atop the other and cut a straight line through the C shape to split each C shape into THREE pieces. This gives you 6 donut pieces (though they may not all have the same weight). You then line these up on the table and cut horizontally through them all, and you get 12 pieces.

How do you split a cake into 6 pieces?

Cut #1 – Down the center of the cake (vertically) leaving two equal halves. Cut #2 – Across the center of the cake (horizontally) leaving four equal slices. Cut #3 – Through the middle edge of the cake slicing all four of the pieces in equal halves, leaving eight equal slices (four equal tops and four equal bottoms).

What is the minimum cuts of circle?

No more cuts are required as the circle is already divided into four equal parts. A single cut is required at 330 degree to divide the circle in three equal parts.

Why does the birthday person cut the cake?

It can be traced back to the Ancient Greeks who burned candles as offerings to their gods and goddesses. For birthdays, they baked round honey cakes to symbolize the moon and topped them off with candles as a special way to pay tribute to the moon goddess, Artemis.

How many queries are required for envy-free cake-cutting?

of queries needed for producing an envy-free allocation. For two agents, the famous cut- and-choose protocol requires only two queries. For three agents, the procedure of Selfridge and Conway [5] guarantees an envy-free allocation after at most 14 queries have been made.

What is the envy free cake cutting problem?

An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource (“cake”) that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation.

What does N stand for in fair division?

When there are N parties equally dividing something, that fair share would be 1/N. For example, if there were 4 parties, each would be entitled to a fair share of ¼ = 25% of the whole. More specifically, they are entitled to a share that they value as 25% of the whole.

Is it better to be the divider or Chooser?

Given the choice, it is always better to be the chooser than the divider. Lone Divider Method: The Divider/Chooser method only works for two players. For more than two players we can use a method called the Lone Divider method.

What is the last Diminisher method?

From Wikipedia, the free encyclopedia. The last diminisher procedure is a procedure for fair cake-cutting. It involves a certain heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over different parts of the cake.

What is the lone divider method?

The lone divider procedure is a procedure for proportional cake-cutting. It involves a heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over different parts of the cake.

What is the lone Chooser method?

In the lone-chooser method, One player is designated to be the chooser. The other players are the dividers. They divide the assets among themselves (details to follow). Then each of the dividers divides his share into equal subshares. The chooser then chooses one subshare from each of the dividers.

How do you use a marker method?

The Method of Markers

1. Preliminaries – The items are lined up in a random order.
2. Step 1 (Bidding) – Each player independently divides the array of items into N segments by placing N-1 markers along the array.
3. Step 2 (Allocations) – Scan the line of items from left to right until the first first marker is located.

What is the method of markers?

The method of markers is a discrete fair-division procedure that is used when there are many more items than there are players and the similarly valued items can be lined up. Players mark sections of the lineup that they feel are equal in value.

How much of an item a player thinks they are entitled to?

players, each player is entitled to at least 1/3 of S. If these assumptions are not met, the division may not be totally fair. What is a fair share? The basic idea in a continuous fair division game is that S is divided into pieces.