Input/Output Problem #1
The basis for this problem is that you did to make an optimal pattern so that all inputted sequences will be "accepted" if they fit the rules of the problem and "rejected" if they break any of them.
.
Above are some examples of functions that can be performed. (A) shows a machine that will only accept the sequences that repeat 12 as you must begin at start and end on a red dot.
In (B) the "*" means you can pass along that route without an input there. So (B) accepts 1111122222, 22222, 1122 etc but doesn't accept any sequence in which there is a 1 after the 2.
In (C) you can move along either route to reach an end. So 12222 and 1333 are both accepted sequences.
All routes have to be either single digit or single letter. Obviously shorthand like "odd", "even" can be used in answers rather than drawing loads of arrows.
Problem #1
Make an optimal machine using digits 0-9 that only accepts sequences where the digits sum are even and rejects if they are odd.
mathematics
asked Nov 14 '18 at 10:58
Ben Franks
50214
add a comment |
The basis for this problem is that you did to make an optimal pattern so that all inputted sequences will be "accepted" if they fit the rules of the problem and "rejected" if they break any of them.
.
Above are some examples of functions that can be performed. (A) shows a machine that will only accept the sequences that repeat 12 as you must begin at start and end on a red dot.
In (B) the "*" means you can pass along that route without an input there. So (B) accepts 1111122222, 22222, 1122 etc but doesn't accept any sequence in which there is a 1 after the 2.
In (C) you can move along either route to reach an end. So 12222 and 1333 are both accepted sequences.
All routes have to be either single digit or single letter. Obviously shorthand like "odd", "even" can be used in answers rather than drawing loads of arrows.
Problem #1
Make an optimal machine using digits 0-9 that only accepts sequences where the digits sum are even and rejects if they are odd.
mathematics
asked Nov 14 '18 at 10:58
Ben Franks
50214
7
These things are called Finite State Machines, and requiring the simplest FSM makes a great puzzle, so I guess this puzzle type is one of the rare cases that would be on topic both here and on PCG. Nicely done!
– Bass
Nov 14 '18 at 11:38
add a comment |
The basis for this problem is that you did to make an optimal pattern so that all inputted sequences will be "accepted" if they fit the rules of the problem and "rejected" if they break any of them.
.
Above are some examples of functions that can be performed. (A) shows a machine that will only accept the sequences that repeat 12 as you must begin at start and end on a red dot.
In (B) the "*" means you can pass along that route without an input there. So (B) accepts 1111122222, 22222, 1122 etc but doesn't accept any sequence in which there is a 1 after the 2.
In (C) you can move along either route to reach an end. So 12222 and 1333 are both accepted sequences.
All routes have to be either single digit or single letter. Obviously shorthand like "odd", "even" can be used in answers rather than drawing loads of arrows.
Problem #1
Make an optimal machine using digits 0-9 that only accepts sequences where the digits sum are even and rejects if they are odd.
mathematics
asked Nov 14 '18 at 10:58
Ben Franks
50214
The basis for this problem is that you did to make an optimal pattern so that all inputted sequences will be "accepted" if they fit the rules of the problem and "rejected" if they break any of them.
.
Above are some examples of functions that can be performed. (A) shows a machine that will only accept the sequences that repeat 12 as you must begin at start and end on a red dot.
In (B) the "*" means you can pass along that route without an input there. So (B) accepts 1111122222, 22222, 1122 etc but doesn't accept any sequence in which there is a 1 after the 2.
In (C) you can move along either route to reach an end. So 12222 and 1333 are both accepted sequences.
All routes have to be either single digit or single letter. Obviously shorthand like "odd", "even" can be used in answers rather than drawing loads of arrows.
Problem #1
Make an optimal machine using digits 0-9 that only accepts sequences where the digits sum are even and rejects if they are odd.
mathematics
mathematics
asked Nov 14 '18 at 10:58
Ben Franks
50214
asked Nov 14 '18 at 10:58
Ben Franks
50214
edited Nov 14 '18 at 11:58
asked Nov 14 '18 at 10:58
Ben Franks
50214
asked Nov 14 '18 at 10:58
Ben Franks
50214
asked Nov 14 '18 at 10:58
Ben Franks
50214
50214
7
These things are called Finite State Machines, and requiring the simplest FSM makes a great puzzle, so I guess this puzzle type is one of the rare cases that would be on topic both here and on PCG. Nicely done!
– Bass
Nov 14 '18 at 11:38
add a comment |
7
These things are called Finite State Machines, and requiring the simplest FSM makes a great puzzle, so I guess this puzzle type is one of the rare cases that would be on topic both here and on PCG. Nicely done!
– Bass
Nov 14 '18 at 11:38
7
7
These things are called Finite State Machines, and requiring the simplest FSM makes a great puzzle, so I guess this puzzle type is one of the rare cases that would be on topic both here and on PCG. Nicely done!
– Bass
Nov 14 '18 at 11:38
These things are called Finite State Machines, and requiring the simplest FSM makes a great puzzle, so I guess this puzzle type is one of the rare cases that would be on topic both here and on PCG. Nicely done!
– Bass
Nov 14 '18 at 11:38
add a comment |
3 Answers
3
active
oldest
votes
Would this work?
Left part is "odd", right part is "even".
answered Nov 14 '18 at 11:17
jafe
17.1k244171
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
This works:
Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
add a comment |
I believe this solution should work:
Where even means "even digit" and odd means "odd digit". Left node is START.
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
Your Answer
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3 Answers
3
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oldest
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3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Would this work?
Left part is "odd", right part is "even".
answered Nov 14 '18 at 11:17
jafe
17.1k244171
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
Would this work?
Left part is "odd", right part is "even".
answered Nov 14 '18 at 11:17
jafe
17.1k244171
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
Would this work?
Left part is "odd", right part is "even".
answered Nov 14 '18 at 11:17
jafe
17.1k244171
Would this work?
Left part is "odd", right part is "even".
answered Nov 14 '18 at 11:17
jafe
17.1k244171
answered Nov 14 '18 at 11:17
jafe
17.1k244171
answered Nov 14 '18 at 11:17
jafe
17.1k244171
answered Nov 14 '18 at 11:17
jafe
17.1k244171
17.1k244171
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
Correct well done, stay tuned for some more (and harder) ones.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
This works:
Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
add a comment |
This works:
Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
add a comment |
This works:
Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
This works:
Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
answered Nov 14 '18 at 11:18
u_ndefined
2,638436
2,638436
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
add a comment |
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
Correct solution +1. But jafe did answer first so I have given him the solution point.
– Ben Franks
Nov 14 '18 at 11:35
add a comment |
I believe this solution should work:
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
I believe this solution should work:
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
I believe this solution should work:
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
I believe this solution should work:
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
edited Nov 14 '18 at 11:17
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
answered Nov 14 '18 at 11:16
NudgeNudge
1,801727
1,801727
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
You can shrink this by one state.
– Gareth McCaughan♦
Nov 14 '18 at 11:17
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
I'm not sure you can, I'll give it a little thought. The other solutions have one fewer node but I'm not sure you can use the same node as start and end (because then an empty string would be a correct one?)
– NudgeNudge
Nov 14 '18 at 11:18
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
Solution works but can be optimised to use less points.
– Ben Franks
Nov 14 '18 at 11:36
add a comment |
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7
These things are called Finite State Machines, and requiring the simplest FSM makes a great puzzle, so I guess this puzzle type is one of the rare cases that would be on topic both here and on PCG. Nicely done!
– Bass
Nov 14 '18 at 11:38