This logic puzzle asks solvers to discover a row of twenty-four flower plants from west to east, identifying both the variety of each plant, as well as the number of blooms on it. One possible logical path is as follows:
The first and second clues establish that there are twenty-four total plants, consisting of six varieties, each of which appears between three and five times. The ninth clue requires there to be at most three snapdragon plants, while the sixteenth clue establishes that there are also three rose plants, since no plants of the same variety can be adjacent to each other. Likewise, clue fifteen establishes that there are four violet plants. The only way to distribute the remaining three varieties into fourteen locations is to have four, five, and five carnations, crocuses, and sunflowers, not necessarily in that order.
Clue seven reveals that one variety of flower only has eight total blooms. Since every plant must have a different number of blooms, the minimum number of blooms from a variety with four plants is ten, so the eight blooms must either be snapdragons or roses. Since clue seventeen states that there is no snapdragon plant has a single bloom, the minimum number of snapdragon blooms is nine, so there must be only eight rose blooms.
Due to the spacing of the rose plants given in clue sixteen, as well as the eighth clue requiring exactly one rose plant between positions 11-16 and the twelfth clue’s requirement that two of the three placements must be prime, the roses must either be in positions 5, 8, and 11 or 7, 10, and 13. Since the twentieth clue states plant 10 has five carnations, the rose plants must be in positions 5, 8, and 11, with the plant in position 11 having one bloom, and the other two plants must either have two and five blooms or three and four blooms.
Combining the nineteenth and eighth clues reveals that there are seven carnations in position 13 and seven of something else in position 4. The thirteenth clue gives the total number of sunflowers as twenty-two, and the seventeenth clue says that one of the sunflower plants only has one bloom. There is no way for the four remaining sunflower plants to add up to twenty-one unless one of them is the other plant with seven blooms in position 4. Additionally, by clue eight, one of the other sunflower plants has six blooms. This means that the remaining two plants must have a total of eight blooms, while having between two and five blooms – in other words, they must have three and five blooms.
The sixth clue tells that three of the plants from positions 19-24 are sunflowers, but position 24 contains violets. Thus, there are sunflowers in positions 19, 21, and 23. The previous step reveals that they must have one, three, and five blooms in some order.
Knowing that there is a rose plant in position 8, clue fifteen prevents there from being a violet plant in position 1. Therefore, the eighteenth clue requires three snapdragons in position 1, six violets in position 24, and another violet plant in position 17. The only remaining pairs of empty spaces with a distance of seven that include a number from 11-16 are 7 and 14, as well as 15 and 22. Either clue five or clue twelve can be used to place the other two violet plants in positions 7 and 14 – the latter of which has one bloom.
Clues eight and nine give only one option for the remaining two snapdragon plants – positions 12 and 20. Since the snapdragon plant in position 12 has two blooms, the one in 20 must have four blooms, per clue six. leaving plant 22 with two blooms.
The 23rd plant must have one, three, or five sunflowers. By the eighth clue, the fifteenth and sixteenth plants are two crocuses and six sunflowers in some order. Applying the tenth clue reveals that there are four roses in position 5, three sunflowers in position 23, and two crocuses in position 16. This also forces six sunflowers in position 15. Since there are a total of eight rose blooms, the plant in position 8 must have the remaining three.
All of the snapdragons, sunflowers, roses and violets have been placed. Since position 22 is required to have two blooms, it cannot be crocuses (thanks to there already being a plant with two crocus blooms), so it must be a carnation plant. Since there are at least four crocus plants, clue fourteen prevents the plant in position 16 from being the easternmost crocus, so there must be a crocus in position 18. There is also a crocus in position 9, since it is adjacent to a carnation.
The seventh clue sets the total number of blooms at eighty-six. With eight of them being roses, nine being snapdragons, and twenty-two being sunflowers, that only leaves forty-seven for carnations, crocuses, and violets. From clue eleven, the number of carnation blooms must be divisible by seven. The three plants so far already sum to fourteen, so there must be two more carnation plants with a total of seven blooms, giving twenty-one total carnations. With four crocus plants, the smallest multiple of seven possible is fourteen, leaving only twelve total violet blooms.
Since there are already violet plants with one and six blooms, the violet in position 7 must have two blooms, and the one in position 17 must have three. The crocus in position 9 must have one bloom, while the one in position 18 has five, forcing one sunflower in position 19, and five in position 21. The crocus with six blooms is either in position 2 or 3, and clue five forces it into position 3.
The remaining two carnation plants are in positions 2 and 6. Clue seventeen says that there is no carnation plant with a single bloom, so the two remaining plants must have three and four, with the four blooms in position 2 and the three blooms in position 6.
The final order of the plants from left to right is:
- 1 – Snapdragon (3 blooms)
- 2 – Carnation (4)
- 3 – Crocus (6)
- 4 – Sunflower (7)
- 5 – Rose (4)
- 6 – Carnation (3)
- 7 – Violet (2)
- 8 – Rose (3)
- 9 – Crocus (1)
- 10 – Carnation (5)
- 11 – Rose (1)
- 12 – Snapdragon (2)
- 13 – Carnation (7)
- 14 – Violet (1)
- 15 – Sunflower (6)
- 16 – Crocus (2)
- 17 – Violet (3)
- 18 – Crocus (5)
- 19 – Sunflower (1)
- 20 – Snapdragon (4)
- 21 – Sunflower (5)
- 22 – Carnation (2)
- 23 – Sunflower (3)
- 24 – Violet (6)
Solvers can index into the type of flower by the number of blooms to spell out the phrase ANSWER IS CARNIVOROUS PLANT. The answer is CARNIVOROUS PLANT.