Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).
Question:-Who has which garden and what is grown where?
Hints
They grow 12 different varieties.
Everybody grows exactly 4 different varieties
Each variety is at least in one garden.
Only one variety is in 4 gardens.
Only in one garden are all 3 kinds of crops.
Only in one garden are all 4 varieties of one kind of crops.
Pear is only in the two border gardens.
Paul's garden is in the middle with no lily.
Aster grower doesn't grow vegetables.
Rose growers don't grow parsley.
Nuts grower has also gourd and parsley.
In the first garden are apples and cherries.
Only in two gardens are cherries.
Sam has onions and cherries.
Luke grows exactly two kinds of fruit.
Tulip is only in two gardens.
Apple is in a single garden.
Only in one garden next to Zick's is parsley.
Sam's garden is not on the border.
Hank grows neither vegetables nor asters.
Paul has exactly three kinds of vegetable.
ANSWER
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Hank
Sam
Paul
Zick
Luke
Variety-1
Apples
Onions
Rose
Aster
Pears
Variety-2
Cherries
Cherries
carrot
Rose
Nuts
Variety-3
Pears
Rose
Gourd
Tulip
Gourd
Variety-4
Rose
Tulip
Onion
Lily
Parsley
SOLUTION
From the puzzle description, we can find below information Garden Owners (Paul , Hank ,Sam, Zick, Luke ), Fruit Varieties (Apple, Pear, Nut, Cherry), Vegetable varieties(Carrot, Parsley, Gourd, Onion) Flower Varieties(Aster, Rose, Tulip, Lily).
We have to follow table approach to solve this puzzle. Choosing right columns and rows is very crucial , without right table we can never solve the puzzle. Always read puzzle carefully and choose table rows&columns appropriately. if we fail here, next steps goes in wrong direction
Since Gardens are in certain order we should take them as Columns.
For rows initially i thought of taking 3 rows for each crop type fruits, flowers and vegetables and fill the table with hints to solve the puzzle (like below), but it is wrong approach to solve puzzle since each garden can have more than one variety from each crop type. This can be understand after reading hints from puzzle description
Wrong Table
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Fruit
Flower
Vegetable
So based on below hint, i have formulated correct table with crop varieties as rows.
==>Everybody grows exactly 4 different varieties
Correct Table
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Variety-1
Variety-2
Variety-3
Variety-4
First fill the table from the direct hints ==>In the first garden are apples and cherries. ==>Paul's garden is in the middle with no lily. ==>Pear is only in the two border gardens.
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Paul
Variety-1
Apples
Pears
Variety-2
Cherries
Variety-3
Pears
Variety-4
Now there are no direct hints, so try to find the hint which are related to other hints ==>Apple is in a single garden. ==>Only in two gardens are cherries. ==>Sam has onions and cherries. Apples and Cherries are in Garden-1 Cherries are in Sam's garden (Which is not Garden-1 since Sam's garden is not on the border.) So No more Apples and cherries exists in Other Gardens
Now From hint ==>Luke grows exactly two kinds of fruit. and also Luke don't own Garden-1 because it has 3 fruits so Luke must grow two remaining fruits Pears and Nuts and from hint ==>Pear is only in the two border gardens. Luke is in Garden-5 and grows Pears and Nuts and from hint ==> Nuts grower has also gourd and parsley.
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Paul
Luke
Variety-1
Apples
Pears
Variety-2
Cherries
Nuts
Variety-3
Pears
Gourd
Variety-4
Parsley
From Hint ==>Only in one garden next to Zick's is parsley. We can conclude Garden-4 belongs to Zick ==>Sam's garden is not on the border. So Garden-2 belongs to Sam and first garden belongs to Hank ==>Sam has onions and cherries.
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Hank
Sam
Paul
Zick
Luke
Variety-1
Apples
Onions
Pears
Variety-2
Cherries
Cherries
Nuts
Variety-3
Pears
Gourd
Variety-4
Parsley
Now take below hint and try to find garden what satisfies this condition in elimination method. ==>Only in one garden are all 4 varieties of one kind of crops. Garden-2, 5 not satisfies above rule ,it already have different kind of crop Garden-3 also not satisfies because of condition ==>Paul has exactly three kinds of vegetable.
Now eliminate one garden from Garden-1 and Garden-4
Garden-1 already have 3 fruits and it can have other fruit variey Nuts also and satisfy the Condition but , If garden has Nuts it will fail at condition ==>Nuts grower has also gourd and parsley. So Garden-4 has all same kind of crops ( crop can be either flowers or vegetables ) Let's determine it has flowers or vegetables crop ==>Hank grows neither vegetables nor asters. ==>Aster grower doesn't grow vegetables ==> Paul has exactly three kinds of vegetable. From Above hints we can say Asters must be in Garden-4 So Garden-4 has all Flowers
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Hank
Sam
Paul
Zick
Luke
Variety-1
Apples
Onions
Aster
Pears
Variety-2
Cherries
Cherries
Rose
Nuts
Variety-3
Pears
Tulip
Gourd
Variety-4
Lily
Parsley
Now find the variety that will be in 4 gardens to satisfy the hint ==>Only one variety is in 4 gardens Garden-4 and Garden-5 columns are already filled up with no common variety. so if one variety from these columns (Aster,Rose.Tulip,Lily,Pears,Nuts,Gourd,Parsley) fits into other 3 gardens. then above hint will be satisfied ==>Only in one garden next to Zick's is parsley ==>Hank grows neither vegetables nor asters. so Gourd,Parsley,Asters are eliminated ==>Pear is only in the two border gardens so pears eliminated ==>Nuts grower has also gourd and parsley. So Nuts also wont fit to have in four gardens ==>Tulip is only in two gardens. ==>Paul's garden is in the middle with no lily. So Tulip and Lily also eliminated So Rose is the one that will be in four gardens If above logic is little complicated to understand, please take each variety and eliminate one by one with help of hints to find variety that will be in 4 gardens.
Garden-1
Garden-2
Garden-3
Garden-4
Garden-5
Owner
Hank
Sam
Paul
Zick
Luke
Variety-1
Apples
Onions
Rose
Aster
Pears
Variety-2
Cherries
Cherries
Rose
Nuts
Variety-3
Pears
Rose
Tulip
Gourd
Variety-4
Rose
Lily
Parsley
From hints fill complete table ==>Tulip is only in two gardens. ==>Paul has exactly three kinds of vegetable.
==>Only in one garden next to Zick's is parsley.
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