Question 15
A beaver has 16 fir trees of four types, four of each type. Trees of the same type have the same height, and different types have different heights.
He plants the 16 trees in a 4×4 garden so that every type appears exactly once in each row and column. Around the garden he places signs giving the number of trees visible along the row or column from each position. Shorter trees behind taller ones are hidden. The pictures below give an example of sign values for a planting.
Editable example, with I shortest and IV tallest:
| I | IV | II | III |
|---|---|---|---|
| IV | I | III | II |
| III | II | IV | I |
| II | III | I | IV |
Example clues: top 2,1,3,2; bottom 3,2,2,1; left 2,1,2,3; right 2,3,2,1. The separate side-view example has heights III,I,II,IV, so two are visible from the left and one from the right.
The following picture gives some signs around the garden.
| Side | Counts in order |
|---|---|
| Top, left to right | 3,2,1,2 |
| Bottom, left to right | 1,2,3,2 |
| Left, top to bottom | 3,2,2,1 |
| Right, top to bottom | 2,1,3,3 |
A=(row 4,column 1), B=(2,1), C=(3,4), D=(1,2). Which four trees below could respectively occupy A,B,C,D?
He plants the 16 trees in a 4×4 garden so that every type appears exactly once in each row and column. Around the garden he places signs giving the number of trees visible along the row or column from each position. Shorter trees behind taller ones are hidden. The pictures below give an example of sign values for a planting.
Editable example, with I shortest and IV tallest:
| I | IV | II | III |
|---|---|---|---|
| IV | I | III | II |
| III | II | IV | I |
| II | III | I | IV |
Example clues: top 2,1,3,2; bottom 3,2,2,1; left 2,1,2,3; right 2,3,2,1. The separate side-view example has heights III,I,II,IV, so two are visible from the left and one from the right.
The following picture gives some signs around the garden.
| Side | Counts in order |
|---|---|
| Top, left to right | 3,2,1,2 |
| Bottom, left to right | 1,2,3,2 |
| Left, top to bottom | 3,2,2,1 |
| Right, top to bottom | 2,1,3,3 |
A=(row 4,column 1), B=(2,1), C=(3,4), D=(1,2). Which four trees below could respectively occupy A,B,C,D?
Heights in increasing-rank notation: IV,III,I,II.
Heights in increasing-rank notation: I,II,IV,III.
Heights in increasing-rank notation: IV,II,I,III.
Heights in increasing-rank notation: IV,I,II,III.