Rita, George, Rachel and Bob each have a different colored bike. The bikes are red, blue, green and black. No one has a bike in a color that begins with the first letter of their name. Bob's bike is not red and Rita's is not blue. What color is Rachel's bike?
Question
Rita, George, Rachel and Bob each have a different colored bike. The bikes are red, blue, green and black. No one has a bike in a color that begins with the first letter of their name. Bob's bike is not red and Rita's is not blue. What color is Rachel's bike?
Solution
Let's solve this step by step:
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No one has a bike in a color that begins with the first letter of their name. So, Rita can't have the Red bike, George can't have the Green bike, Rachel can't have the Red bike, and Bob can't have the Blue bike.
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Bob's bike is not red. So, Bob must have the Green bike (since he can't have the Blue bike from step 1).
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Rita's bike is not blue. So, Rita must have the Black bike (since she can't have the Red bike from step 1).
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Now, George can't have the Green bike (from step 1) and the Black bike is taken by Rita. So, George must have the Blue bike.
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Finally, Rachel can't have the Red bike (from step 1), the Green bike is taken by Bob, and the Blue bike is taken by George. So, Rachel must have the Black bike. But the Black bike is already taken by Rita. So, there seems to be a mistake in the question or in the steps we've taken to solve it.
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