The Flaky Engineer

[Yoruichi-san]

I'm baking biscuits. I have 15 cubic inches of dough. I need to roll it out and cut circles out of it. Let's say I'm obsessive and require the circles to be perfect 3 inch rounds, and I am uber-skilled and rolling and roll to a perfectly uniform thickness of 1/4 inch, and I have some strange compulsion and can only roll the dough into rectangular shapes.

Being an engineer, on a day when I'm more lazy and less greedy, I choose to roll the dough out once, cut the rounds, and feed the scraps to the dog. What are dimensions so that I can cut the maximum biscuits? (Hey, I said less greedy... )

On a day when I'm more greedy and less lazy, I make a quadruple batch (60 cubic inches) and choose to roll the dough out, cut the rounds, consolidate the scraps and roll out again, cut more rounds, etc until I am left with less dough than I can roll into a piece I can cut a biscuit out of, and I feed that to the dog. What is the minimum number of times I have to roll out the dough?

[bonanova]

Assuming 3" is the diameter and not the radius, your 60 in² of dough area can accommodate differing number of close-packed rows:

Height = 3" Length= 20" gives one row of six biscuits.

Height = 5.6" Length = 10.7" gives two rows of three biscuits [you'd need 12" to get four and three.

Height = 8.2" Length = 7.31" gives three rows of two, one and two biscuits.[you'd need 7.5" to get rows of two, two and two.

Either of the first two heights gives six biscuits, and that seems to be the maximum.

Fido gets fed about 4.4 in³ of dough.

But this answer makes me think I'm missing something.

[CaptainEd]

I'm missing something even before I try to answer: I see actions of

* cutting into rounds

* rolling out

* rolling into rectangles

* requiring 1/4 inch thick rollout

I think I hear that you cut them into circles, then roll them into 1/4 thickness, and then roll them into rectangular shapes. This will necessarily reduce the thickness. But maybe the 1/4 thickness is required AFTER rolling the rounds into rectangular shapes?

Please, what is the sequence of events and constraints thereupon? Alternatively, what was the stuff about rectangular shapes about?

[k-man]

For the first part I agree with Bonanova's answer. There doesn't seem to be a way to get more than 6 biscuits out of 60 sq. inches of dough.

For the second part, I can do it in 3 rolls/cuts. First roll it out in a 15x16 rectangle. this will allow you to cut out 27 biscuits (3 rows or 5 plus 3 rows of 4). It leaves approx. 49.148 square inches of dough left. Second, you roll the remaining dough into a 15x3.276 rectangle and cut 5 more biscuits leaving you with 13.8 square inches for one more biscuit. You get a total of 33 biscuits and your dog gets approximately 1.68 cubic inches of dough.

@CaptainEd

The last paragraph of the OP kinda describes the sequence. First you roll out the dough into a rectangular shape 1/4 inch thick. Then you cut out the round biscuits. The remaining dough either goes to the dog or get reshaped into another rectangle for the next round of cutting.

[CaptainEd]

Thanks, k-man. That makes perfect sense, and I don't see why I didn't get that from Y-san's exposition--I think I need more biscuits this morning...

[jhawk]

Roll 3 times.

1st roll yields 26 biskets from 10.9" x 22" rectangle. Area remaining 56.3

2nd roll yields 6 biskets from 5.6" x 10" rectangle ,, Area remaining 13.9

3rd roll yield 1 bisket from 3" x 3" square Area reaining 5.8

Dog eats 5.8 sqin, or 1.4 cubic in

Sorry, can't get spoilere to work