Think of it as a riddle.
You need to eliminate and match one city to one transport to one person in the end.
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Take a look at my diagram!*
Use each clue to eliminate the rows and columns until you have narrowed it down.
Below is my work. It would be too hard to explain every step of the way; it will work differently for everyone. Maybe look up the game "Telepathy". The concept is similar!
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I first read the instructions, eliminating and boxing the possible and impossible options.
If I ever got down to one empty spot in a column or row, I'd make sure to circle that and frequently write it down.
If you're doing this right, you will always be progressing. Don't doubt yourself; don't overthink it. It's the game of narrowing down and elimination. If you find yourself stuck, write what you know down. Use logic. Make sure you always look for rows that you forgot to cross out, or empty spots that you missed. Reread the instructions! You will get there!
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*The "eliminated" part is a bit confusing, they weren't entirely eliminated. It's just my thought process! I didn't continue to use it. Just remember to group the right things together!
Don't be scared of looking up the cities and if you don't know, their states!
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Conclusion:
John arrived by plane to Saint Louis meet up with his nephew.
John arrived by bus to Denver to visit his brother.
John came by train to Miami to visit his uncle.
John rode a cycle to Boston to meet up with his cousin.
John drove in a car to San Fransisco to visit his parents.
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Please let me know if you have any questions, or if this helped!