Input/Output Problem #1












12












$begingroup$


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







share|improve this question











$endgroup$








  • 7




    $begingroup$
    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!
    $endgroup$
    – Bass
    Nov 14 '18 at 11:38
















12












$begingroup$


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







share|improve this question











$endgroup$








  • 7




    $begingroup$
    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!
    $endgroup$
    – Bass
    Nov 14 '18 at 11:38














12












12








12





$begingroup$


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







share|improve this question











$endgroup$




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






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Nov 14 '18 at 11:58







Ben Franks

















asked Nov 14 '18 at 10:58









Ben FranksBen Franks

50214




50214








  • 7




    $begingroup$
    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!
    $endgroup$
    – Bass
    Nov 14 '18 at 11:38














  • 7




    $begingroup$
    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!
    $endgroup$
    – Bass
    Nov 14 '18 at 11:38








7




7




$begingroup$
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!
$endgroup$
– Bass
Nov 14 '18 at 11:38




$begingroup$
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!
$endgroup$
– Bass
Nov 14 '18 at 11:38










3 Answers
3






active

oldest

votes


















9












$begingroup$

Would this work?




Left part is "odd", right part is "even".

enter image description here







share|improve this answer









$endgroup$













  • $begingroup$
    Correct well done, stay tuned for some more (and harder) ones.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36



















6












$begingroup$

This works:




enter image description here

Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8







share|improve this answer









$endgroup$













  • $begingroup$
    Correct solution +1. But jafe did answer first so I have given him the solution point.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:35



















5












$begingroup$

I believe this solution should work:




enter image description here Where even means "even digit" and odd means "odd digit". Left node is START.







share|improve this answer











$endgroup$













  • $begingroup$
    You can shrink this by one state.
    $endgroup$
    – Gareth McCaughan♦
    Nov 14 '18 at 11:17










  • $begingroup$
    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?)
    $endgroup$
    – NudgeNudge
    Nov 14 '18 at 11:18












  • $begingroup$
    Solution works but can be optimised to use less points.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36











Your Answer





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3 Answers
3






active

oldest

votes








3 Answers
3






active

oldest

votes









active

oldest

votes






active

oldest

votes









9












$begingroup$

Would this work?




Left part is "odd", right part is "even".

enter image description here







share|improve this answer









$endgroup$













  • $begingroup$
    Correct well done, stay tuned for some more (and harder) ones.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36
















9












$begingroup$

Would this work?




Left part is "odd", right part is "even".

enter image description here







share|improve this answer









$endgroup$













  • $begingroup$
    Correct well done, stay tuned for some more (and harder) ones.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36














9












9








9





$begingroup$

Would this work?




Left part is "odd", right part is "even".

enter image description here







share|improve this answer









$endgroup$



Would this work?




Left part is "odd", right part is "even".

enter image description here








share|improve this answer












share|improve this answer



share|improve this answer










answered Nov 14 '18 at 11:17









jafejafe

18.6k352181




18.6k352181












  • $begingroup$
    Correct well done, stay tuned for some more (and harder) ones.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36


















  • $begingroup$
    Correct well done, stay tuned for some more (and harder) ones.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36
















$begingroup$
Correct well done, stay tuned for some more (and harder) ones.
$endgroup$
– Ben Franks
Nov 14 '18 at 11:36




$begingroup$
Correct well done, stay tuned for some more (and harder) ones.
$endgroup$
– Ben Franks
Nov 14 '18 at 11:36











6












$begingroup$

This works:




enter image description here

Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8







share|improve this answer









$endgroup$













  • $begingroup$
    Correct solution +1. But jafe did answer first so I have given him the solution point.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:35
















6












$begingroup$

This works:




enter image description here

Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8







share|improve this answer









$endgroup$













  • $begingroup$
    Correct solution +1. But jafe did answer first so I have given him the solution point.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:35














6












6








6





$begingroup$

This works:




enter image description here

Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8







share|improve this answer









$endgroup$



This works:




enter image description here

Here odd means 1,3,5,7,9 / and even means 0,2,4,6,8








share|improve this answer












share|improve this answer



share|improve this answer










answered Nov 14 '18 at 11:18









u_ndefinedu_ndefined

2,638436




2,638436












  • $begingroup$
    Correct solution +1. But jafe did answer first so I have given him the solution point.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:35


















  • $begingroup$
    Correct solution +1. But jafe did answer first so I have given him the solution point.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:35
















$begingroup$
Correct solution +1. But jafe did answer first so I have given him the solution point.
$endgroup$
– Ben Franks
Nov 14 '18 at 11:35




$begingroup$
Correct solution +1. But jafe did answer first so I have given him the solution point.
$endgroup$
– Ben Franks
Nov 14 '18 at 11:35











5












$begingroup$

I believe this solution should work:




enter image description here Where even means "even digit" and odd means "odd digit". Left node is START.







share|improve this answer











$endgroup$













  • $begingroup$
    You can shrink this by one state.
    $endgroup$
    – Gareth McCaughan♦
    Nov 14 '18 at 11:17










  • $begingroup$
    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?)
    $endgroup$
    – NudgeNudge
    Nov 14 '18 at 11:18












  • $begingroup$
    Solution works but can be optimised to use less points.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36
















5












$begingroup$

I believe this solution should work:




enter image description here Where even means "even digit" and odd means "odd digit". Left node is START.







share|improve this answer











$endgroup$













  • $begingroup$
    You can shrink this by one state.
    $endgroup$
    – Gareth McCaughan♦
    Nov 14 '18 at 11:17










  • $begingroup$
    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?)
    $endgroup$
    – NudgeNudge
    Nov 14 '18 at 11:18












  • $begingroup$
    Solution works but can be optimised to use less points.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36














5












5








5





$begingroup$

I believe this solution should work:




enter image description here Where even means "even digit" and odd means "odd digit". Left node is START.







share|improve this answer











$endgroup$



I believe this solution should work:




enter image description here Where even means "even digit" and odd means "odd digit". Left node is START.








share|improve this answer














share|improve this answer



share|improve this answer








edited Nov 14 '18 at 11:17

























answered Nov 14 '18 at 11:16









NudgeNudgeNudgeNudge

1,846728




1,846728












  • $begingroup$
    You can shrink this by one state.
    $endgroup$
    – Gareth McCaughan♦
    Nov 14 '18 at 11:17










  • $begingroup$
    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?)
    $endgroup$
    – NudgeNudge
    Nov 14 '18 at 11:18












  • $begingroup$
    Solution works but can be optimised to use less points.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36


















  • $begingroup$
    You can shrink this by one state.
    $endgroup$
    – Gareth McCaughan♦
    Nov 14 '18 at 11:17










  • $begingroup$
    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?)
    $endgroup$
    – NudgeNudge
    Nov 14 '18 at 11:18












  • $begingroup$
    Solution works but can be optimised to use less points.
    $endgroup$
    – Ben Franks
    Nov 14 '18 at 11:36
















$begingroup$
You can shrink this by one state.
$endgroup$
– Gareth McCaughan♦
Nov 14 '18 at 11:17




$begingroup$
You can shrink this by one state.
$endgroup$
– Gareth McCaughan♦
Nov 14 '18 at 11:17












$begingroup$
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?)
$endgroup$
– NudgeNudge
Nov 14 '18 at 11:18






$begingroup$
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?)
$endgroup$
– NudgeNudge
Nov 14 '18 at 11:18














$begingroup$
Solution works but can be optimised to use less points.
$endgroup$
– Ben Franks
Nov 14 '18 at 11:36




$begingroup$
Solution works but can be optimised to use less points.
$endgroup$
– Ben Franks
Nov 14 '18 at 11:36


















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