TimeSpaceLightForce

not certain if this is what you mean.

that can result to a conical cut and damage this works..(unless one of the bear notice that the middle layer has damage unlike the upper and lower layer) but the cutting blade length is just twice the radius (as shown) so the spinning cut of 0 deg bent knife can only divide into 2 parts.

@Phi for All -little bear's drink ain't ready yet like the forks,knives and napkins. -good guessing of cake . But no need to cut layered cake between layers since they were separated already. -If the in between material is tough the length of the U shaped cutting knife you proposed shall be more than twice the diameter of the cake.

@Phi for All -No, 2 drinks,a whole round cake,clues. And the candle (maybe a red herring). -yes, the slice is a single movement of blade (not the tapered edge) in one direction..horizontal,vertical or rotational.

oh..actually the transparent bottle is not a donut.

@Phi for All -yes she can follow the marks..or make new ones needlessly. -she can use the bent knife ..or straighten it again before or after the cut. -yes,"already" means hurrying her by cutting once and the no cut have been made yet. @NimrodTheGoat -maybe that is why they are fat. @DrKrettin -the illustration was done with excel inserted ellipses and polygons. I can't do Goldilock's hair. (see illustration for clues)

Momma bear asked Goldilock to divide the whole round cake into 3 equal pieces. So The girl marked 3 equally distanced points around its perimeter in order to make 3 slices from the center (where the candle is) to the markers. But before she can do the first slice Poppa bear asked her to do it with just 2 slices if she can. So Goldilock bent the knife into 120 degrees angle in order to make a 1/3 piece on first slice (with knife vertex on the center) and two more equal 1/3 pieces from the remaining part with the second slice.But before she can do the first slice Little bear asked her to do it already with only 1 slice. So how did Goldilock divide the cake into 3 equal pieces with a single slice? (see illustration)

Taking all glasses off the scale does not count as using it once.

@uncool- I thought it was 340122240 which is I just remembered is the product computed for "answered" . Since un=1/9 , 37791360 really answers this problem. Note that I have posted this in this section 4 years ago but it was unanswered (no reply). -It started with the anagram "one+twelve=two+eleven" ..as I could remember.

@imatfaal- thanks for clarifying that factors are Integers..I took the wrong term and it should be " If letters are values to multiply in equations:" so on.. @Raider5678-I see now why you think it is impossible. Because factors are not fractions. All the letter values are correct! You'll just get it answered.. (the error is somewhere in the multiplication for the product)

@imatfaal-why should the factors(letters) be all whole numbers?

@Raider- if (z)(e)(r )(o)=0 maybe not "all" of those factors are equal to zero. one= o X n X e

If letters are factors of equations: zero = 0 one = 1 two = 2 three = 3 four = 4 five = 5 six = 6 seven = 7 eight = 8 nine = 9 ten = 10 twelve = 12 fifteen = 15 twenty = 20 thirty = 30 forty = 40 sixty = 60 hundred = 100 thousand = 1000 million = 1000000 billion = 1000000000 What is the product for unanswered = ?

The balance on top of scale is clever. I accept it. Using it once give 2 readings but required 2 trials only. The solutions I had in mind are as ff: 1) 4 trials using scale OR balance. 2) 2 trials each using scale AND balance.

@bmad - there are some same length distances to decide where to turn.. diagonal of [4 x 5] = straight [1 x 6 ] , only one way is counted

@bmad That's too many for the succeeding trips(moves) to be getting farther than the last one.

@Sriman Dutta There are 12 golden eggs.. arranged according to shell thickness and with tags in troy weights. Tags 1,2,3..12 are troy units. No two eggs have same mass or weight. -Right! There are 66 ways that two of these eggs can be swapped or exchange shelf position. Find a way to sort the two misplaced gold eggs.. with weighing scale or the balance scale or both.

@ Sensei "'Divide 12 pieces by 2, with 6 units each, then measure mass, on weight, 6 eggs on the left, 6 eggs on the right. If their mass is equal it means gold egg is in each of 6 units." -All are golden eggs with varying weights..1-12 troys

correcting. **allowed queen/pawn move or any other move as long start at one center ..ends on another. Any angle as long as distances keep increasing.

Blunderboar kept and watches his 12 golden eggs.. arranged according to shell thickness and with tags in troy weights. He told Jack (his captive) to seek the two gold eggs that he swapped from the shelves using the available machines with the least tries. If Jack succeed he shall become a servant.. else the giant's supper. What method must the boy execute?

@Daecon -Any time -thus cant be trice neither -By P.T. -trajectory curve (center to center of two squares)