BOX BASED PUZZLES
Eight boxes namely H to O are placed in a rack one above the other. The lowermost rack is numbered as 1 and above is 2 and so on. Each of the boxes is having different colors among Blue, Green, Yellow, Red, White, Orange, Indigo and Red. Each of the boxes is having different serial numbers among 19, 23, 17, 31, 34, 37, 27 and 21. All the above information is not necessarily in the same order.
There are three boxes are placed between the box which having serial number as 27 and the Indigo colored box. Box J’s serial number is not 27. The Indigo colored box is placed adjacent to blue colored box. Box I’s serial number is 37 and doesn’t placed at the topmost rack. Box M is Yellow colored and placed adjacent to the Red colored box. Box H is placed in the even numbered rack above fourth and it is placed adjacent to box which has serial number as 31. Not more than five boxes are placed above the Red colored box. Box J is placed in the seventh rack and Box H is placed adjacent to Box J. Two boxes are placed between the boxes having the serial number 21 and 34. Box J is White colored. Maximum numbers of boxes are placed between the Brown colored box and Orange colored box. Box H is not Brown colored. Box L is Green colored and it is placed adjacent to the Orange colored box. Box N’s serial number is 21 and placed in the lowermost rack. The box which has serial number as 23 is placed three boxes above the Yellow colored box. Box O’s serial number is 19. The box which has serial number as 17 is placed above the box which has serial number as 34 .
Final table:
| Case-2-B |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box O |
Brown |
19 |
| 7 |
Box J |
White |
23 |
| 6 |
Box H |
Indigo |
17 |
| 5 |
Box K |
Blue |
31 |
| 4 |
Box M |
Yellow |
34 |
| 3 |
Box I |
Red |
37 |
| 2 |
Box L |
Green |
27 |
| 1 |
Box N |
Orange |
21 |
Common Explanation
References:
Box N’s serial number is 21 and placed in the lowermost rack.
Two boxes are placed between the boxes having the serial number 21 and 34.
Box J is placed in the seventh rack and Box H is placed adjacent to Box J.
Box J is White colored.
Box H is placed in the even numbered rack above fourth and it is placed adjacent to box which has serial number as 31.
Box J’s serial number is not 27.
Inferences:
From above statements,
First 2 statements can be directly filled in the table as shown.
Box J is White colored and it is placed in the 7th rack (reference points 3 & 4)
Box H can be placed either 8th or 6th floor (above 4th floor & adjacent to 7th floor). Thus we get two possibilities (reference points 3 & 5)
Case-1: Box H is placed in the 8th rack and Box J’s serial number is 31 as per statement.
Case-2: Box H is placed in the 6th rack and either Box J’s serial number is 31 or the box which is placed in 5th rack is serial numbered as 31 as per statement.
Note: Box J’s serial number is not 27.
By using above information, we get the following table as shown,
| Case-1 |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box H |
|
|
| 7 |
Box J |
White |
31 |
| 6 |
|
|
|
| 5 |
|
|
|
| 4 |
|
|
34 |
| 3 |
|
|
|
| 2 |
|
|
|
| 1 |
Box N |
|
21 |
| Case-2 |
| Rack |
Box |
Color |
Serial Number |
| 8 |
|
|
|
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
|
|
| 5 |
|
|
31 |
| 4 |
|
|
34 |
| 3 |
|
|
|
| 2 |
|
|
|
| 1 |
Box N |
|
21 |
References:
Maximum numbers of boxes are placed between the Brown colored box and Orange colored box.
Box L is Green colored and it is placed adjacent to the Orange colored box.
Box H is not Brown colored.
Inferences:
From above statements,
With respect to the 1st reference point, Brown and Orange colored box is placed in topmost and lowermost rack (not necessarily in the same order). By this 6 boxes (maximum possibility) can be placed between Brown and Orange colored box.
We know, Box J is White colored and it is placed in the 7th rack. So Orange colored box can’t be place at 8th rack since Orange colored box is placed adjacent to Green colored box (Box L). Therefore Brown colored box is placed at 8th rack (topmost) and Orange colored box is placed at 1st rack (lowermost) i.e. Box N as per table in both cases (reference point 2)
Box L is Green colored and it is placed in 2nd rack in both cases (reference point 2)
By using 3rd reference point Case-1 gets eliminated since Box H is not Brown colored.
By using above information, we get the following table as shown,
Case-1 [Eliminated]
Box H is not Brown colored. |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box H |
Brown |
|
| 7 |
Box J |
White |
31 |
| 6 |
|
|
|
| 5 |
|
|
|
| 4 |
|
|
34 |
| 3 |
|
|
|
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
| Case-2 |
| Rack |
Box |
Color |
Serial Number |
| 8 |
|
Brown |
|
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
|
|
| 5 |
|
|
31 |
| 4 |
|
|
34 |
| 3 |
|
|
|
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
References:
Box I’s serial number is 37 and doesn’t placed at the topmost rack.
Inferences:
From above statements,
Note: We get 2 more possibilities from case-2 by using 1st reference point as shown.
Case-2: Here, Box J’s serial number is 31. Box I’s serial number is 37 and it is placed in 5th rack
Case-2-A: Here, Box J’s serial number is 31. Box I’s serial number is 37 and it is placed in 3rd rack
Case-2-B: Here, the box which is placed in the 5th rack is serial numbered as 31. Box I’s serial number is 37 and it is placed in 3rd rack.
By using above information, we get the following table as shown,
| Case-2 |
| Rack |
Box |
Color |
Serial Number |
| 8 |
|
Brown |
|
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
|
|
| 5 |
Box I |
|
37 |
| 4 |
|
|
34 |
| 3 |
|
|
|
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
| Case-2-A |
| Rack |
Box |
Color |
Serial Number |
| 8 |
|
Brown |
|
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
|
|
| 5 |
|
|
|
| 4 |
|
|
34 |
| 3 |
Box I |
|
37 |
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
| Case-2-B |
| Rack |
Box |
Color |
Serial Number |
| 8 |
|
Brown |
|
| 7 |
Box J |
White |
|
| 6 |
Box H |
|
|
| 5 |
|
|
31 |
| 4 |
|
|
34 |
| 3 |
Box I |
|
37 |
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
References:
Box M is Yellow colored and placed adjacent to the Red colored box.
The box which has serial number as 23 is placed three boxes above the Yellow colored box.
Not more than five boxes are placed above the Red colored box.
Box O’s serial number is 19.
Inferences:
From above statements,
Case-2: Here, Box M is Yellow colored and it must be placed in 3rd rack and the box which has serial numbered as 23 is placed in 6th rack (only possibility) i.e. Box H as per table (two boxes are placed between Box M and Box H (serial number 23)). Red colored box is placed in the 4th rack (reference points 1, 2 and 3 gets satisfied). Now, Box O is placed in 8th rack (only possibility) and its serial number is 19 (reference point 4 satisfied)
Case-2-A: Here, Box M is Yellow colored and it must be placed in 5th rack and the box which has serial numbered as 23 is placed in 8th rack (only possibility) (two boxes are placed between Box M and the box which has serial number as 23). Red colored box is placed either in the 4th rack or 6th rack (reference points 1, 2 and 3 gets satisfied). Now there is no place for Box O (serial number is 19). Hence this case become invalid and it can be eliminated.
| Case-2 |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box O |
Brown |
19 |
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
|
23 |
| 5 |
Box I |
|
37 |
| 4 |
|
Red |
34 |
| 3 |
Box M |
Yellow |
|
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
Case-2-A [Eliminated]
No place for Box O (serial number is 19) |
| Rack |
Box |
Color |
Serial Number |
| 8 |
|
Brown |
23 |
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
Red |
|
| 5 |
Box M |
Yellow |
|
| 4 |
|
Red |
34 |
| 3 |
Box I |
|
37 |
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
Case-2-B: Here, Box O is placed in 8th rack (only possibility) and its serial number is 19 (reference point 4 satisfied). Now, Box M is Yellow colored and it must be placed in 4th rack and the box which has serial numbered as 23 is placed in 7th rack (only possibility) i.e. Box J as per table (two boxes are placed between Box M and Box J (serial number 23)). Red colored box is placed either in the 5th rack or 3rd rack (reference points 1, 2 and 3 gets satisfied).
By using above information we get the following cases as shown below,
| Case-2-B |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box O |
Brown |
19 |
| 7 |
Box J |
White |
23 |
| 6 |
Box H |
|
|
| 5 |
|
Red |
31 |
| 4 |
Box M |
Yellow |
34 |
| 3 |
Box I |
Red |
37 |
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
References:
The box which has serial number as 17 is placed above the box which has serial number as 34.
There are three boxes are placed between the box which having serial number as 27 and the Indigo colored box.
The Indigo colored box is placed adjacent to blue colored box.
Inferences:
From above statements,
Case-2: Here there is no place for the box which has serial number as 17 above the box which has serial number as 34 (reference point 1). Hence this case become invalid and it can be eliminated.
Case-2-B: Here, the box which has serial number as 17 are placed in 6th racks i.e. Box H as per table (reference point 1). Finally, the Box L’s serial number must be 27 (only number left among given) and it is placed in 2nd rack. Now, Indigo colored box is placed at 6th rack (reference point 2 satisfied). Blue colored box is placed in 5th rack (only possibility) since Indigo colored box is placed adjacent to blue colored box (reference point 3 satisfied). Finally, Box K is placed in 5th rack and Red colored box is placed in 3rd rack. Thus all the above conditions satisfied and we get the completed table as shown below.
Case-2 [Eliminated]
Box (serial number 17) is placed above the box (serial number 34) [not satisfied] |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box O |
Brown |
19 |
| 7 |
Box J |
White |
31 |
| 6 |
Box H |
|
23 |
| 5 |
Box I |
|
37 |
| 4 |
|
Red |
34 |
| 3 |
Box M |
Yellow |
|
| 2 |
Box L |
Green |
|
| 1 |
Box N |
Orange |
21 |
| Case-2-B |
| Rack |
Box |
Color |
Serial Number |
| 8 |
Box O |
Brown |
19 |
| 7 |
Box J |
White |
23 |
| 6 |
Box H |
Indigo |
17 |
| 5 |
Box K |
Blue |
31 |
| 4 |
Box M |
Yellow |
34 |
| 3 |
Box I |
Red |
37 |
| 2 |
Box L |
Green |
27 |
| 1 |
Box N |
Orange |
21 |