So it's your birthday!
And the round thing with candles on it is from Carvel's.

You blow out the candles in one try, and your wish comes true!
A personalized BrainDen puzzle - which, unfortunately,
you must answer correctly before eating the sweet cold stuff.

It's French vanilla ice cream, covered with dark Swiss chocolate icing.

A protractor is provided, which is set at random to an angle X.
You must cut a piece at that angle, turn the piece upside down and replace it.
Because it's made of ice cream, it heals itself [re-freezes].

You then cut a 2^{nd} piece, at angle Xbeginning where the 1^{st} piece ended, and turn it upside down. Beginning where the 2^{nd} piece ends, a 3^{rd} piece at angle X is cut and flipped. And so on.
Each successive piece begins at angle [n-1]X and ends at angle nX, [shown] leaving a path of vanilla ice cream in its wake.

Eventually you will work your way around the cake and begin
cutting into the part of the cake that has been flipped upside down.
When that is flipped, of course, the chocolate icing comes back on top.

Here's the puzzle. If the cut-and-flip-at-angle-X process is continued, will there ever come a point where the cake is restored to its original state?

Answer correctly, and we all have cake.
Otherwise, it's wait until next year.

Since

X was chosen at random, the probability that it is rational is zero.

## Question

## bonanova 85

So it's your birthday!

And the round thing with candles on it is from Carvel's.

You blow out the candles in one try, and your wish comes true!

A personalized BrainDen puzzle - which, unfortunately,

you must answer

correctlybefore eating the sweet cold stuff.It's French vanilla ice cream, covered with dark Swiss chocolate icing.

A protractor is provided, which is set

at randomto an angle.XYou must cut a piece at that angle, turn the piece upside down and replace it.

Because it's made of ice cream, it heals itself [re-freezes].

You then cut a 2

^{nd}piece, at anglebeginning where the 1X^{st}piece ended, and turn it upside down.Beginning where the 2

^{nd}piece ends, a 3^{rd}piece at angleis cut and flipped. And so on.XEach successive piece begins at angle [

n-1]and ends at angleXn, [shown] leaving a path of vanilla ice cream in its wake.XEventually you will work your way around the cake and begin

cutting into the part of the cake that has been flipped upside down.

When that is flipped, of course, the chocolate icing comes back on top.

Here's the puzzle. If the cut-and-flip-at-angle-

process is continued,Xwill there ever come a point where the cake is restored to its original state?

Answer correctly, and we all have cake.

Otherwise, it's wait until next year.

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