The Numbered Neighbors Puzzle - Solution

What was the puzzle?

As we know, AJ, Celeste, Juan, Kara, Lily, and Randy all live on Redwood Avenue. Each of their house numbers has three digits, but the only digits in their house numbers are 2, 3, 5, and 6 with repetition of digits in house number allowed. 

Let's have all the given clues once again here.

1. AJ's house number is Juan's house number doubled. 

2. Juan lives next to Lily and right across from Randy. 

3. Randy's number is the lowest on the street. 

4. Celeste's number is a higher number than AJ's but has the same three digits as his. They both have the same digit in the hundreds place.
 
5. Kara's house number is the reverse of Juan's.

STEPS : 

1] As per (1), AJ's house number is double of Juan's house number. From the given sets of digits i.e. 2, 3, 5, 6, this is only possible if there is 3 at third place of Juan's house number and 6 at third place of AJ's house number.

That is AJ's house number is XX6 and that of Juan's is XX3.

2] As we can see carry is not being forwarded from Juan's house number XX3 while getting doubled to give AJ's house number. So, it's clear that, the number formed by first two digits of AJ's house number is exactly double of the number formed by first two digits of Juan's house number.

From the given set of digits 2, 3, 5, 6, possible house numbers of AJ and Juan are 666 & 333 or 526 & 263.

If AJ is having house number 666, then as per (4), there would be no valid house number left for Celeste using digits 2, 3, 5, 6.

Therefore, AJ's house number must be 526 and that of Juan's must be 263

3] Now, as per (2), Randy must be having house number 262.

4] As per (4), Celeste's house number must be 5XX. Since, his house number has same digits as that of AJ's but higher than AJ's house number, he must be having house number 562.

5] As per (5), Kara's house number is reverse of Juan's. Therefore, Kara's house number is 362.

6] And as per (2), for the fact that Juan is living next to the Lily to be true, Lily must have house number 265 using the given set of digits 2, 3, 5, 6.

CONCLUSION :

The street addresses of all are listed as below - 

AJ         : 526, Redwood Avenue.
 
Celeste : 562, Redwood Avenue.
 
Juan     : 263, Redwood Avenue.
 
Kara     : 362, Redwood Avenue.
 
Lily       : 265, Redwood Avenue.
 
Randy   : 262, Redwood Avenue.