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What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks ?
- a)3
- b)5
- c)7
- d)9
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the smallest number of ducks that could swim in this formation...
Clearly, the smallest such number is 3.
Three ducks can be arranged as shown above to satisfy all the three given conditions.
Most Upvoted Answer
What is the smallest number of ducks that could swim in this formation...
Solution:
The given formation can be represented as follows:
D D _ D D
where D represents a duck and _ represents a space.
Let's assume that there are n ducks in total.
1. Two ducks in front of a duck:
This means that the first three places in the formation are occupied by ducks. Therefore, we can say that n ≥ 3.
D D D _ _ _ _ _ _
2. Two ducks behind a duck:
This means that the last three places in the formation are occupied by ducks. Therefore, we can say that n ≥ 3.
_ _ _ _ _ _ D D D
3. A duck between two ducks:
This means that there is at least one duck in the middle of the formation. Therefore, we can say that n ≥ 3.
_ _ _ D _ D _ _ _
Combining all three conditions, we get:
n ≥ 3 + 3 + 1
n ≥ 7
Therefore, the smallest number of ducks that can swim in this formation is 7. Hence, option (c) is incorrect.
The next smallest possible number of ducks is 8, which can be represented as follows:
D D D _ _ _ D D _
_ D D _ _ _ D D D
However, both of these formations do not fit the given criteria exactly, as there are more than two ducks between two ducks in each case.
The only remaining option is 3 ducks, which can be represented as follows:
D D _ D _ D
_ D D _ D D
This formation satisfies the given criteria, and therefore, the smallest number of ducks that can swim in this formation is 3. Hence, the correct answer is option (a).
The given formation can be represented as follows:
D D _ D D
where D represents a duck and _ represents a space.
Let's assume that there are n ducks in total.
1. Two ducks in front of a duck:
This means that the first three places in the formation are occupied by ducks. Therefore, we can say that n ≥ 3.
D D D _ _ _ _ _ _
2. Two ducks behind a duck:
This means that the last three places in the formation are occupied by ducks. Therefore, we can say that n ≥ 3.
_ _ _ _ _ _ D D D
3. A duck between two ducks:
This means that there is at least one duck in the middle of the formation. Therefore, we can say that n ≥ 3.
_ _ _ D _ D _ _ _
Combining all three conditions, we get:
n ≥ 3 + 3 + 1
n ≥ 7
Therefore, the smallest number of ducks that can swim in this formation is 7. Hence, option (c) is incorrect.
The next smallest possible number of ducks is 8, which can be represented as follows:
D D D _ _ _ D D _
_ D D _ _ _ D D D
However, both of these formations do not fit the given criteria exactly, as there are more than two ducks between two ducks in each case.
The only remaining option is 3 ducks, which can be represented as follows:
D D _ D _ D
_ D D _ D D
This formation satisfies the given criteria, and therefore, the smallest number of ducks that can swim in this formation is 3. Hence, the correct answer is option (a).
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Community Answer
What is the smallest number of ducks that could swim in this formation...
There are only 3 ducks
1
2
3
And 1,2 duck is in front of 3
2,3 duck is back of 1
And 2 duck is the middle one
1
2
3
And 1,2 duck is in front of 3
2,3 duck is back of 1
And 2 duck is the middle one
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