I have some fruits in a basket. All except two are bananas, all except two are apples and all except two are oranges. How many fruits are there in the basket
is this like an Escher basket...
one banana , one apple , one orange
To solve this problem, we can use a technique called "logical deduction".
Let's assume that there are x bananas, y apples, and z oranges in the basket.
According to the given information:
- "All except two are bananas" means that the total number of fruits (x + y + z) minus 2 equals the number of bananas (x).
- "All except two are apples" means that the total number of fruits minus 2 equals the number of apples (y).
- "All except two are oranges" means that the total number of fruits minus 2 equals the number of oranges (z).
So we have three equations:
1. x + y + z - 2 = x
2. x + y + z - 2 = y
3. x + y + z - 2 = z
Simplifying each equation:
1. y + z = 2
2. x + z = 2
3. x + y = 2
Now we can solve this system of equations to find the values of x, y, and z.
From equation 1, we have y + z = 2. Since there are no negative fruit counts, the possible combinations of y and z are {1, 1} and {0, 2}.
Case 1: y = 1 and z = 1
Plugging these values into equation 2, we have x + 1 = 2, which means x = 1.
Case 2: y = 0 and z = 2
Plugging these values into equation 2, we have x + 2 = 2, which means x = 0.
Therefore, there are two possible solutions:
- Solution 1: x = 1 (bananas), y = 1 (apples), z = 1 (oranges). Total fruits = 1 + 1 + 1 = 3.
- Solution 2: x = 0 (bananas), y = 0 (apples), z = 2 (oranges). Total fruits = 0 + 0 + 2 = 2.
So, there are either 3 or 2 fruits in the basket depending on the possible solutions.