Mixing
I have knowledge of where a collection of hours sit relative to each other on a clock. I wish to find the...
$begingroup$
So I have a collection of equations in arithmetic mod $12$.
$A-C = 2$
$B-D = 2$
$C-E = 3$
$A neq B$
$B neq C$
$C neq D$
$D neq E$
$F-H = 4$
$F neq G$
$G neq H$
$K-M = 2$
$J-L = 3$
$J neq K$
$K neq L$
$L neq M$
$N-Q = 2$
$P-R = 2$
$Q-S = 2$
$R-T = 3$
$S-U = 2$
$N neq P$
$P neq Q$
$Q neq R$
$R neq S$
$S neq T$
$T neq U$
Now since these equations allow for the values to all be shifted by a constant offset and still get a valid result we will assume for simplicity that $A = 0$ in this scenario. That still doesn't give a unique solution methinks but the context I believe should allow for that based on what I've been told.
These values come from a clock-life puzzle I've been trying to solve and the solution will show where all these points sit relative to each other on a clock face. From that an order can be derived that solves the puzzle itself. However, this can be distilled to just a math question, so I only provided that information for context purposes.
algebra-precalculus modular-arithmetic
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
$endgroup$
|
show 3 more comments
$begingroup$
So I have a collection of equations in arithmetic mod $12$.
$A-C = 2$
$B-D = 2$
$C-E = 3$
$A neq B$
$B neq C$
$C neq D$
$D neq E$
$F-H = 4$
$F neq G$
$G neq H$
$K-M = 2$
$J-L = 3$
$J neq K$
$K neq L$
$L neq M$
$N-Q = 2$
$P-R = 2$
$Q-S = 2$
$R-T = 3$
$S-U = 2$
$N neq P$
$P neq Q$
$Q neq R$
$R neq S$
$S neq T$
$T neq U$
Now since these equations allow for the values to all be shifted by a constant offset and still get a valid result we will assume for simplicity that $A = 0$ in this scenario. That still doesn't give a unique solution methinks but the context I believe should allow for that based on what I've been told.
These values come from a clock-life puzzle I've been trying to solve and the solution will show where all these points sit relative to each other on a clock face. From that an order can be derived that solves the puzzle itself. However, this can be distilled to just a math question, so I only provided that information for context purposes.
algebra-precalculus modular-arithmetic
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
$endgroup$
1
$begingroup$
You are asking.... for a solution? Just put it into a computer.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:21
$begingroup$
@MorganRodgers how? Do you have a modular arithmetic algebra calculator lying around somewhere? If so I'd be more than happy to see it. Afaik here there isn't a unique solution. In fact, my picking A = 0 only nails down C = 10 and E = 7. I don't see how it actually solves the other values uniquely.
$endgroup$
– The Great Duck
Jan 14 at 6:27
$begingroup$
Python can do it.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:28
1
$begingroup$
If it doesn't nail down the other values, you need to exhaustively go over all possibilities (either by hand or using a computer). So are you asking for someone to do this for you? Or do you have some confusion about how it would be done? (My comment wasn't saying it's a pointless question, just that it is unclear what your question is)
$endgroup$
– Morgan Rodgers
Jan 14 at 6:29
1
$begingroup$
There are TONS of solutions. About a million, even with $A$, $F$, $J$, and $N$ all $=0$.
$endgroup$
– Morgan Rodgers
Jan 14 at 17:25
|
show 3 more comments
$begingroup$
So I have a collection of equations in arithmetic mod $12$.
$A-C = 2$
$B-D = 2$
$C-E = 3$
$A neq B$
$B neq C$
$C neq D$
$D neq E$
$F-H = 4$
$F neq G$
$G neq H$
$K-M = 2$
$J-L = 3$
$J neq K$
$K neq L$
$L neq M$
$N-Q = 2$
$P-R = 2$
$Q-S = 2$
$R-T = 3$
$S-U = 2$
$N neq P$
$P neq Q$
$Q neq R$
$R neq S$
$S neq T$
$T neq U$
Now since these equations allow for the values to all be shifted by a constant offset and still get a valid result we will assume for simplicity that $A = 0$ in this scenario. That still doesn't give a unique solution methinks but the context I believe should allow for that based on what I've been told.
These values come from a clock-life puzzle I've been trying to solve and the solution will show where all these points sit relative to each other on a clock face. From that an order can be derived that solves the puzzle itself. However, this can be distilled to just a math question, so I only provided that information for context purposes.
algebra-precalculus modular-arithmetic
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
$endgroup$
So I have a collection of equations in arithmetic mod $12$.
$A-C = 2$
$B-D = 2$
$C-E = 3$
$A neq B$
$B neq C$
$C neq D$
$D neq E$
$F-H = 4$
$F neq G$
$G neq H$
$K-M = 2$
$J-L = 3$
$J neq K$
$K neq L$
$L neq M$
$N-Q = 2$
$P-R = 2$
$Q-S = 2$
$R-T = 3$
$S-U = 2$
$N neq P$
$P neq Q$
$Q neq R$
$R neq S$
$S neq T$
$T neq U$
Now since these equations allow for the values to all be shifted by a constant offset and still get a valid result we will assume for simplicity that $A = 0$ in this scenario. That still doesn't give a unique solution methinks but the context I believe should allow for that based on what I've been told.
These values come from a clock-life puzzle I've been trying to solve and the solution will show where all these points sit relative to each other on a clock face. From that an order can be derived that solves the puzzle itself. However, this can be distilled to just a math question, so I only provided that information for context purposes.
algebra-precalculus modular-arithmetic
algebra-precalculus modular-arithmetic
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
asked Jan 14 at 6:13
The Great DuckThe Great Duck
21632047
21632047
1
$begingroup$
You are asking.... for a solution? Just put it into a computer.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:21
$begingroup$
@MorganRodgers how? Do you have a modular arithmetic algebra calculator lying around somewhere? If so I'd be more than happy to see it. Afaik here there isn't a unique solution. In fact, my picking A = 0 only nails down C = 10 and E = 7. I don't see how it actually solves the other values uniquely.
$endgroup$
– The Great Duck
Jan 14 at 6:27
$begingroup$
Python can do it.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:28
1
$begingroup$
If it doesn't nail down the other values, you need to exhaustively go over all possibilities (either by hand or using a computer). So are you asking for someone to do this for you? Or do you have some confusion about how it would be done? (My comment wasn't saying it's a pointless question, just that it is unclear what your question is)
$endgroup$
– Morgan Rodgers
Jan 14 at 6:29
1
$begingroup$
There are TONS of solutions. About a million, even with $A$, $F$, $J$, and $N$ all $=0$.
$endgroup$
– Morgan Rodgers
Jan 14 at 17:25
|
show 3 more comments
1
$begingroup$
You are asking.... for a solution? Just put it into a computer.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:21
$begingroup$
@MorganRodgers how? Do you have a modular arithmetic algebra calculator lying around somewhere? If so I'd be more than happy to see it. Afaik here there isn't a unique solution. In fact, my picking A = 0 only nails down C = 10 and E = 7. I don't see how it actually solves the other values uniquely.
$endgroup$
– The Great Duck
Jan 14 at 6:27
$begingroup$
Python can do it.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:28
1
$begingroup$
If it doesn't nail down the other values, you need to exhaustively go over all possibilities (either by hand or using a computer). So are you asking for someone to do this for you? Or do you have some confusion about how it would be done? (My comment wasn't saying it's a pointless question, just that it is unclear what your question is)
$endgroup$
– Morgan Rodgers
Jan 14 at 6:29
1
$begingroup$
There are TONS of solutions. About a million, even with $A$, $F$, $J$, and $N$ all $=0$.
$endgroup$
– Morgan Rodgers
Jan 14 at 17:25
1
1
$begingroup$
You are asking.... for a solution? Just put it into a computer.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:21
$begingroup$
You are asking.... for a solution? Just put it into a computer.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:21
$begingroup$
@MorganRodgers how? Do you have a modular arithmetic algebra calculator lying around somewhere? If so I'd be more than happy to see it. Afaik here there isn't a unique solution. In fact, my picking A = 0 only nails down C = 10 and E = 7. I don't see how it actually solves the other values uniquely.
$endgroup$
– The Great Duck
Jan 14 at 6:27
$begingroup$
@MorganRodgers how? Do you have a modular arithmetic algebra calculator lying around somewhere? If so I'd be more than happy to see it. Afaik here there isn't a unique solution. In fact, my picking A = 0 only nails down C = 10 and E = 7. I don't see how it actually solves the other values uniquely.
$endgroup$
– The Great Duck
Jan 14 at 6:27
$begingroup$
Python can do it.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:28
$begingroup$
Python can do it.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:28
1
1
$begingroup$
If it doesn't nail down the other values, you need to exhaustively go over all possibilities (either by hand or using a computer). So are you asking for someone to do this for you? Or do you have some confusion about how it would be done? (My comment wasn't saying it's a pointless question, just that it is unclear what your question is)
$endgroup$
– Morgan Rodgers
Jan 14 at 6:29
$begingroup$
If it doesn't nail down the other values, you need to exhaustively go over all possibilities (either by hand or using a computer). So are you asking for someone to do this for you? Or do you have some confusion about how it would be done? (My comment wasn't saying it's a pointless question, just that it is unclear what your question is)
$endgroup$
– Morgan Rodgers
Jan 14 at 6:29
1
1
$begingroup$
There are TONS of solutions. About a million, even with $A$, $F$, $J$, and $N$ all $=0$.
$endgroup$
– Morgan Rodgers
Jan 14 at 17:25
$begingroup$
There are TONS of solutions. About a million, even with $A$, $F$, $J$, and $N$ all $=0$.
$endgroup$
– Morgan Rodgers
Jan 14 at 17:25
|
show 3 more comments
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1
$begingroup$
You are asking.... for a solution? Just put it into a computer.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:21
$begingroup$
@MorganRodgers how? Do you have a modular arithmetic algebra calculator lying around somewhere? If so I'd be more than happy to see it. Afaik here there isn't a unique solution. In fact, my picking A = 0 only nails down C = 10 and E = 7. I don't see how it actually solves the other values uniquely.
$endgroup$
– The Great Duck
Jan 14 at 6:27
$begingroup$
Python can do it.
$endgroup$
– Morgan Rodgers
Jan 14 at 6:28
1
$begingroup$
If it doesn't nail down the other values, you need to exhaustively go over all possibilities (either by hand or using a computer). So are you asking for someone to do this for you? Or do you have some confusion about how it would be done? (My comment wasn't saying it's a pointless question, just that it is unclear what your question is)
$endgroup$
– Morgan Rodgers
Jan 14 at 6:29
1
$begingroup$
There are TONS of solutions. About a million, even with $A$, $F$, $J$, and $N$ all $=0$.
$endgroup$
– Morgan Rodgers
Jan 14 at 17:25