From I and II:
There are two shelves in between the ones of M and G.
| Case 1 | Case 2 | Case 3 | Case 4 |
| M/G | | | |
| M/G | | |
| | M/G | |
| G/M | | | M/G |
| G/M | | |
| | G/M | |
| | | G/M |
N has his shelf immediately above A. D has his shelf immediately above N. So, cases 2 and 3 are invalid.
| Case 1 | Case 4 |
| M/G | D |
| N |
| A |
| G/M | M/G |
| D | |
| N | |
| A | G/M |
E has his shelf above G but not immediately.
There are two shelves in between the ones that belong to T and A. So, case 1 is invalid.
So, E has kept his things immediately below M. Hence, statements I and II together are sufficient.
From II and III:
There are two shelves in between the ones of M and G.
| Case 1 | Case 2 | Case 3 | Case 4 |
| M/G | | | |
| M/G | | |
| | M/G | |
| G/M | | | M/G |
| G/M | | |
| | G/M | |
| | | G/M |
E has his shelf above T. E has his shelf below A but not immediately. There are two shelves in between the ones that belong to T and A.
| Case 1 | Case 2(i) | Case 2(ii) | Case 3 | Case 4 |
| M/G | A | | | |
| M/G | M/G | A | |
| A | E | | M/G | A |
| G/M | T | A | E | M/G |
| E | G/M | G/M | T | E |
| T | | E | G/M | T |
| | T | | G/M |
D has his shelf immediately above N. There is one shelf in between M and N. So, cases 1, 2(ii), 3 are invalid.
| Case 2(i) | Case 4 |
| A | D |
| G | N |
| E | A |
| T | M |
| M | E |
| D | T |
| N | G |
G has his shelf below T and not adjacent to that of D. So, case 2(i) is invalid.
E has kept his things immediately below M. Hence, statements II and III together are sufficient.
From I and III:
There are two shelves in between the ones that belong to T and A.
| Case 1 | Case 2 | Case 3 | Case 4 |
| T/A | | | |
| T/A | | |
| | T/A | |
| A/T | | | T/A |
| A/T | | |
| | A/T | |
| | | A/T |
E has his shelf above G but not immediately. E has his shelf below A but not immediately. So, A must be above T. So, case 4 is invalid. N has his shelf immediately above A. So, case 1 is invalid. There is one shelf in between the ones of A and D.
There is one shelf in between M and N.
| Case 2 | Case 3 |
| N | D/ |
| A | N |
| M | A |
| D | M |
| T | /D |
| T |
| |
E has his shelf above G but not immediately. E has his shelf below A but not immediately. So, case 2 is invalid.
So, E has kept his things immediately below M. So, statements I and III are sufficient together.
Hence, any two of the three statements together are sufficient.
Study Notes
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