Super Lollipop
A candy company just launches a new product called "Super Lollipop"is made of pink, red, green, blue and yellow sugar balls, one of each color, connected together with 4 identical sticks in a tetrahedral fashion, as shown above.
How many types of Super Lollipops can this company make?
The answer is 10.
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1 solution
Relevant wiki: Optical Isomerism
First, by choosing the center sugar ball, we would have 5 choices, and for each choice, there are only 2 mirror images of such possible outcomes as shown below:
Despite their similar appearances, these structures are different because we can never superimpose one 3D-image perfectly upon another no matter how many times we rotate it. Similarly, by comparing our hands, they are mirror images of each other, but both hands are still different as with palms up, the left thumb is on the far left, not on the right as the right thumb. This property is called "chirality" , with root meaning the hands.
Thus, in this question, the Super Lollipop is arranged similar to carbon compound molecule, where the center sugar ball is considered the "Chiral center" for the structure.
Therefore, there are 5 × 2 = 1 0 possible types of Super Lollipops.
Note : The two mirror-imaged "chiral" compounds are called "stereo-isomers". Despite having exactly the same elements and chemical formula, these chiral chemicals may react differently to the same substrate. For example, while one stereo-isomer may be used as a drug component, the other one may not exhibit such effect and can even turn toxic to human body.