Well folks, I hope I re-figured the coins puzzle correctly.
I have flashbacks of taking Finite Math @ University of Tulsa, where the professor didn’t believe in working his examples out ahead of time. He would fill four chalkboards up with one problem, only to realize he’d made a mistake on back on chalkboard one! You could hear the groans clear across campus (and notes being ripped to pieces) as he erased with the heel of his hand and rewrote pieces of the math problem like nothing was wrong. Anyway here’s my solution. I’m sure you guys won’t hesitate to correct me if I’ve made a mistake.
First weighing:
coins 1,2,3,4 ~ 5,6,7,8
Scenerio One
1,2,3,4 = 5,6,7,8 means counterfeit coin is in group 9,10,11,12
You also know that coins 1,2,3,4,5,6,7,8 are good coins, and can be used as a control for further testing. (for reference, “good” coins will be denoted as "")
Weigh 9, ~ 11,12
Scenerio One.One
9,$ = 10,11 means counterfeit coin is 12.
weigh 12 against a good coin to determine if it’s heavy or light.
Scenerio One.Two
9,$ < 10,11 means either 9 is light OR 10 or 11 is heavy
weigh 10 ~ 11, if equal then 9 is light, otherwise heavy side is the fake coin.
Scenerio One.Three
9,$ > 10,11 means either 9 is heavy OR 10 or 11 is light.
weigh 10 ~ 11, if equal, then 9 is heavy, otherwise light side is the fake coin
Scenerio Two (Here’s where it gets good!)
1,2,3,4 < 5,6,7,8 means 1,2,3,4 has a light coin, or 5,6,7,8 has a heavy coin.
You also know that 9,10,11,12 are good coins.
weigh 1,2,5 ~ 3,4,
Scenerio Two.One
1,2,5 = 3,4, means 6,7, or 8 is heavy
weigh 6 ~ 7
Scenerio Two.Two
1,2,5 < 3,4,$ means 1 or 2 is light
weigh 1 ~ 2
Scenerio Two.Three
1,2,5 > 3,4,$ means 5 heavy OR 3 or 4 is light
weigh 3 ~ 4
Scenerio Three
1,2,3,4 > 5,6,7,8 means 1,2,3,4 has a heavy coin or 5,6,7,8 has a light coin
you also know that 9,10,11,12 are good coins
weigh 1,2,5 ~ 3,4,
Scenerio Three.One
1,2,5 = 3,4, means 6,7or 8 is heavy
weigh 6 ~ 7
Scenerio Three.Two
1,2,5 < 3,4,$ means 3 or 4 heavy
weigh 3 ~ 4
Scenerio Three.Three
1,2,5 > 3,4,$ means 1 or 2 is heavy, OR 5 is light
weigh 1 ~ 2
Enright3