Toaster

[Guest]

You have an old-fashioned type toaster, with hinged doors on its two sides. It holds two pieces of bread at once but toasts each of them on one side only. To toast both sides, it is necessary to open the doors and reverse the slices.

It takes three seconds to put a slice of bread into the toaster, three seconds to take it out and three seconds to reverse a slice without removing it. Both hands are required for each of these operations, which means that it is not possible to put in, take out or turn two slices simultaneously. Nor is it possible to butter a slice while another slice is being put into the toaster, turned or taken out. The toasting time for one side of a piece of bread is thirty seconds. It takes twelve seconds to butter a slice.

Each slice is buttered on one side only. No side may be buttered until it has been toasted. A slice toasted and buttered one one side may be returned to the toaster for toasting on the other side. The toaster is warmed up at the start.

The goal is to prepare three slices of hot buttered toast in as little time as possible.

[Guest]

can one side of the toaster starting working before the other side. Something like this, put one bread in one door then toast, put another slice in the other door then toast?

[Guest]

can one side of the toaster starting working before the other side. Something like this, put one bread in one door then toast, put another slice in the other door then toast?

Sure.

[Guest]

I got 132 seconds

load slice 1       3

load slice 2       3

toast 1&2 side 1   30

turn slice 2       3

remove slice 1     3

load slice 3       3

toast 2s2 $ 3s1    30

butter slice 1     during toast cycle

remove slice 2     3

turn slice 3       3

loade slice 1      3

toast 1s2 & 3s2    30

butter slice 2     during toast cycle

remove slice 3     3

remove slice 1     3

butter slice 3     12

TOTAL..............132 seconds

[Guest]

FYI, the best time I've seen is 114 seconds.

[Guest]

	slice 1		slice 2		slice 3


0	in(3)		

3	toasting 1(33)	in(6)

6			toasting 1(36)	butter(18)

18					butter done

33	out(36)

36					in(39)

39			reverse(42)	toasting 1(69)

42	butter(54)	toasting 2(72)

54	butter done

69			out(72)

72					reverse(75)

75	in(78)				toasting 2(105)

78	toasting 2(108)	butter(90)

90			complete

105					out(108)

108	out(111)			complete

111	complete	

that makes 111 seconds to completion (time in parenthesis is the time each task will be completed)

Edited April 8, 2010 by rb01

[Guest]

	slice 1		slice 2		slice 3


0	in(3)		

3	toasting 1(33)	in(6)

6			toasting 1(36)	butter(18)

18					butter done

33	out(36)

36					in(39)

39			reverse(42)	toasting 1(69)

42	butter(54)	toasting 2(72)

54	butter done

69			out(72)

72					reverse(75)

75	in(78)				toasting 2(105)

78	toasting 2(108)	butter(90)

90			complete

105					out(108)

108	out(111)			complete

111	complete	

that makes 111 seconds to completion (time in parenthesis is the time each task will be completed)

No side may be buttered until it has been toasted.

Slice 3 violates this requirement.

[Guest]

	slice 1		slice 2		slice 3


0	in(3)		

3	toasting 1(33)	in(6)

6			toasting 1(36)	butter(18)

18					butter done

33	out(36)

36					in(39)

39			reverse(42)	toasting 1(69)

42	butter(54)	toasting 2(72)

54	butter done

69			out(72)

72					reverse(75)

75	in(78)				toasting 2(105)

78	toasting 2(108)	butter(90)

90			complete

105					out(108)

108	out(111)			complete

111	complete	

that makes 111 seconds to completion (time in parenthesis is the time each task will be completed)

[quote name='kkehoe5' date='08 April 2010 - 07:56 AM' timestamp='1270734967' post='223085']

I got 132 seconds

load slice 1       3

load slice 2       3

toast 1&2 side 1   30

turn slice 2       3

remove slice 1     3

load slice 3       3

toast 2s2 $ 3s1    30

butter slice 1     during toast cycle

remove slice 2     3

turn slice 3       3

loade slice 1      3

toast 1s2 & 3s2    30

butter slice 2     during toast cycle

remove slice 3     3

remove slice 1     3

butter slice 3     12

TOTAL..............132 seconds

My solution is pretty close to the same (I've got to get quicker at typing these in - new ones are posted while I type )

Fun problem, thanks. It's kinda fun to play with aspects of my job in a fun way .

120 seconds - Since a piece starts toasting as soon as it is put in, you can move a little quicker this way:

[Slice, Side, Task, -- Task Time, --- Current Elapsed Time]


(A, 1, in, -- 3, --- 3)

(A, 1, toast, -- 30, --- 33) & (B, 1, in, -- 3, --- 6)

(B, 1, toast, -- 30, --- 36)

(A, x, flip, -- 3, --- 36)

(A, 2, toast, -- 30, --- 66) & (B, 1, out, -- 3, --- 39)

(C, 1, in, -- 3, --- 42)

(C, 1, toast, -- 30, --- 72) & (B, 1, butter, -- 12, --- 51)

(A, 2, out, -- 3, --- 69)

(B, 2, in, -- 3, --- 72)

(B, 2, toast, -- 30, --- 102) & (C, x, flip, -- 3, --- 75)

(C, 2, toast, -- 30, --- 105) & (A, 2, butter, -- 12, --- 87) **Slice A Done**

(B, 2, out, -- 3, --- 105) **Slice B Done**

(C, 2, out, -- 3, --- 108)

(C, 2, butter, -- 12, --- 120) **Slice C done**

***Done*** - 120 seconds total

That looks kind of confusing, I acutally put it in a Gantt Chart to track it all out.

That's as fast as I can get so I'm looking forward to seeing the 114s solution.

I'd been assuming that the toast had to be removed to be buttered, but since a buttered slice can be returned to the toaster, we should be able to assume the bottom is toasting (otherwise you'd have to but the butter down), if this is true - could we not butter the toasted top side of a piece, while it's still in the toaster - toasting the bottom so:

[Slice, Side, Task, -- Task Time, --- Current Elapsed Time]


(A, 1, in, -- 3, --- 3)

(A, 1, toast, -- 30, --- 33) & (B, 1, in, -- 3, --- 6)

(B, 1, toast, -- 30, --- 36)

(A, x, flip, -- 3, --- 36)

(A, 2, toast, -- 30, --- 66) & (B, 1, out, -- 3, --- 39)

(C, 1, in, -- 3, --- 42)

(C, 1, toast, -- 30, --- 72) & (B, 1, butter, -- 12, --- 51)

(A, 2, out, -- 3, --- 69)

(B, 2, in, -- 3, --- 72)

(B, 2, toast, -- 30, --- 102) & (C, x, flip, -- 3, --- 75)

(C, 2, toast, -- 30, --- 105) & (A, 2, butter, -- 12, --- 87) **Slice A Done**

(C, 1, butter, --12, --- 97)

(B, 2, out, -- 3, --- 105) **Slice B Done**

(C, 2, out, -- 3, --- 108) **Slice C done**

***Done*** - 108 seconds total

[Guest]

126 seconds

                    Start     Stop

load slice 1 toast  t=0       t=3

load slice 2 toast  t=3       t=6

remove slice 1      t=33      t=36   

load slice 3        t=36      t=39

remove slice 2      t=39      t=42

butter slice 1      t=42      t=54

load slice 1        t=54      t=57

butter slice 2      t=57      t=69

remove slice 3      t=69      t=72

load slice 2        t=72      t=75

butter slice 3      t=75      t=87

remove slice 1      t=87      t=90

load slice 3        t=90      t=93

remove slice 2      t=105     t=108

remove slice 3      t=123     t=126

Edited April 8, 2010 by kkehoe5

[Guest]

Slice 3 violates this requirement.

Hmm - I can get 120 - curious to see 114

Edited April 8, 2010 by rb01

[Guest]

Best I can get is 117.  Unless you're using a jedi mind trick, the minimum toast & remove time for 1 slice is 36; and the minimum time to toast both sides, in/out,reverse, and butter another piece is (30*2+3*3+12 = 81); so 36+81 = 117 shortest path (assuming all other tasks can interleave, which they can).


	slice 1		slice 2		slice 3


0	in(3)		

3	toasting 1(33)	in(6)

6			toasting 1(36)	

18					

33	out(36)

36					in(39)

39			reverse(42)	toasting 1(69)

42	butter(54)	toasting 2(72)

54	butter done

69					reverse(72)

72			out(75)		toasting 2(102)

75	in(78)				

78	toasting 2(108)	butter(90)

90			complete

102					out(105)

105					butter(117)

108	out(111)			

111	complete			

117					complete	

[Guest]

slice 1 ; slice 2 ; slice 3

0 in(3) ; ;

3 toasting 1(33) ; in(6);

6 ; toasting 1(36) ;

33 remove(36); ;

36 ; ; in(39)

39 ; reverse(42) ; toasting 1(69)

42 butter(54) ; toasting 2(72);

54 butter done ; butter (66);

66 ; butter done;

69 ; ; reverse (72)

72 ; remove (75) ; toasting 2 (102)

75 in(78) ; complete ;

78 toasting 2(108) ; ; butter(90)

90 ; ; butter done

102 ; ; remove(105)

105 out(108) ; ; complete

108 complete ; ;

Edited April 8, 2010 by jlf278

[Guest]

Not spoilered as there is no answer...

The simple sequence:

In, Toast, Out, In, Toast, Flip, Toast, Out, Butter

is 117s, so you can't butter in sequence with any combination of 3 full toasts within 114s.

Therefore some of the operations must be broken up and buttering must be done before toasting both sides of at least two slices.

I've experimented with flipping after half a toast and half toasting and taking out, but can't find a working combination, I've been close in several ways.

[Guest]

Retracted, since Ringer is on the right track.

Edited April 8, 2010 by Drexlin

[Guest]

We can cut down the time if we're allowed to take the toast out before it's finished and then put it back to finish later. Is this allowed?

[Guest]

Retracted, since Ringer is on the right track.

Booooo!!! The toaster door only opens after a complete toast cycle.

[Guest]

My question is does each slice of bread have to be toasted on both sides since the problem did not state it...

[Guest]

My question is does each slice of bread have to be toasted on both sides since the problem did not state it...

Yes, both sides must be toasted.

[Guest]

Alright, someone check this solution for 114 - I feel like it must have a glitch:

003 - Slice A In

006 - Slice B In

018 - Slice B Side 1 (12 seconds)

021 - Slice B Out

024 - Slice C In

033 - Slice A Side 1 (30 seconds) done

036 - Slice A Out

039 - Slice B In && Slice C Side 1 (15 seconds)

042 - Slice C Flip

057 - Slice B Side 1 (30 seconds) done

060 - Slice B Flip

072 - Slice A Side 1 - butter **A butter done**

&&& - Slice C Side 2 (30 seconds) done

075 - Slice C Out

078 - Slice A In

090 - Slice C Side 2 - butter **C butter done**

&&& - Slice B Side 2 (30 seconds) done **B toasted**

093 - Slice B Out 

096 - Slice C In (side 1)

108 - Slice B Side 1or2-butter **B butter done** ^^^B Finished^^^

&&& - Slice A Side 2 (30 seconds) done **A toasted**

111 - Slice A Out ^^^A Finished^^^

&&& - Slice C Side 1 (30 seconds) done **C toasted**

114 - Slice C Out ^^^C Finished^^^

_____*^*^*DONE*^*^*

There are definitly variations on this solution and there could be ways to get it even shorter - but it hits the 114 mark without sticking your hand in the toaster

[Ericho]

I am just so lucky to get 111 s.

[flamebirde]

how did you do that?