My hypothesis is that that peanut butter will take both gums out of each type of hair, because of the oil that is in peanut butter.
Things needed:
Peanut Butter
Vinegar
Rubbing Alcohol
Sugarless Gum
Bubble Gum
Colorless/"Real" Hair
Colored/ "Fake" Hair
First Step:Chew both types of gums!
Second Step:
Put both types of gums in both sets of hair.
Step 3:
Trying to get out bubble gum from "real" hair!
IT WORKED!!!!
The peanut butter will remove gum of both types in the "real"/colorless hair!
Second Step:Put both types of gums in both sets of hair.
Step 3:Apply peanut butter to the hair.
Peanut butter removed sugar free gum from "real" hair.
Peanut butter removed sugar free gum from "real" hair. Trying to get out bubble gum from "real" hair!IT WORKED!!!!The peanut butter will remove gum of both types in the "real"/colorless hair!The peanut butter removed the sugarless gum from the "fake" hair; however it will not remove the bubble gum from the "fake" hair.
PEANUT BUTTER WILL NOT REMOVE FROM "FAKE"/COLORED HAIR!!!!!
Hair soaking in vinegar with gum already in it! 
Remove hair from the vinegar and began trying to get the gum out.
Trying to get the gum free from the "real" hair.
With the vinegar neither the sugar free gum or bubble gum would come out!!!!
Trying to work the sugar free gum out of the "fake"/colored hair.
Could not get ethier piece out of the "fake"/colored hair with vinegar.
In fact, using the vinegar on the "fake"/colored hair made it worse. 
In alcohol took the sugar free gum out of the "real"/colorless hair. 
Did not remove the bubble gum from the "real"/colorless hair. 
The alcohol did not remove the sugar free gum from the "fake"/colored hair nor did it remove the bubble gum.
Finish Product:
Conclusion is that the oil from the peanut butter allows the gum to be removed from hair easier!
PEANUT BUTTER WILL NOT REMOVE FROM "FAKE"/COLORED HAIR!!!!!Hair soaking in vinegar with gum already in it! Remove hair from the vinegar and began trying to get the gum out.Trying to get the gum free from the "real" hair. With the vinegar neither the sugar free gum or bubble gum would come out!!!!Trying to work the sugar free gum out of the "fake"/colored hair.Could not get ethier piece out of the "fake"/colored hair with vinegar.In fact, using the vinegar on the "fake"/colored hair made it worse. In alcohol took the sugar free gum out of the "real"/colorless hair. Did not remove the bubble gum from the "real"/colorless hair. The alcohol did not remove the sugar free gum from the "fake"/colored hair nor did it remove the bubble gum. Finish Product:Conclusion is that the oil from the peanut butter allows the gum to be removed from hair easier!
