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# Tennis Balls are to be placed in nine buckets

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Tennis Balls are to be placed in nine buckets  [#permalink]

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27 Jul 2013, 00:19
1
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25% (medium)

Question Stats:

80% (01:41) correct 20% (02:04) wrong based on 145 sessions

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Tennis balls are to be placed into 9 buckets so that each bucket contains at least one ball, at the request of detail- oriented players. At most, five of the buckets are to contain the same number of balls, and no two of the remaining buckets are to contain an equal number of balls. What is the least possible number of balls needed for the buckets?
A)8
B)14
C)19
D)25
E)30

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Re: Tennis Balls are to be placed in nine buckets  [#permalink]

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27 Jul 2013, 01:28
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Condition: at least one in each, at most five with equal number.

To minimize the overall number, we have to place 1 in five buckets.

$$1-1-1-1-1-...$$

Condition: no other two have the same number of balls, hence we must complete the sequence like this

$$1-1-1-1-1-2-3-4-5$$ => $$Tot=19$$
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Re: Tennis Balls are to be placed in nine buckets  [#permalink]

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27 Jul 2013, 04:00
Zarrolou wrote:
Condition: at least one in each, at most five with equal number.

To minimize the overall number, we have to place 1 in five buckets.

$$1-1-1-1-1-...$$

Condition: no other two have the same number of balls, hence we must complete the sequence like this

$$1-1-1-1-1-2-3-4-5$$ => $$Tot=19$$

HI Thanks for your explanation..To understand a little bit more, can you please tell me how did u approach on the second condition?
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Re: Tennis Balls are to be placed in nine buckets  [#permalink]

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27 Jul 2013, 04:08
1
Pragnya87 wrote:
Zarrolou wrote:
Condition: at least one in each, at most five with equal number.

To minimize the overall number, we have to place 1 in five buckets.

$$1-1-1-1-1-...$$

Condition: no other two have the same number of balls, hence we must complete the sequence like this

$$1-1-1-1-1-2-3-4-5$$ => $$Tot=19$$

HI Thanks for your explanation..To understand a little bit more, can you please tell me how did u approach on the second condition?

From here, we have 4 empty slots

$$1-1-1-1-1-?-?-?-?$$

Can we put 0 balls in the 6th slot ? No because there must be at least one in each.
Can we put 1 ball again in the 6th slot ? No because at most five have the same number of balls.
Can we put 2 balls in the 6th slot ? Yes

From now on you can repeat the reasoning for the 7th slot:

Can we put 0 balls in ? No because there must be at least one in each.
Can we put 1 ball again? No because at most five have the same number of balls.
Can we put 2 balls in ? No, SECOND CONDITION no other two have the same number of balls
Can we put 3 balls in ? Yes

and so on...

At the end we have this: $$1-1-1-1-1-2-3-4-5$$ => $$Tot=19$$

Hope I've explained myself well
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Re: Tennis Balls are to be placed in nine buckets  [#permalink]

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17 May 2017, 17:39
fameatop wrote:
Tennis balls are to be placed into 9 buckets so that each bucket contains at least one ball, at the request of detail- oriented players. At most, five of the buckets are to contain the same number of balls, and no two of the remaining buckets are to contain an equal number of balls. What is the least possible number of balls needed for the buckets?

(A) 8
(B) 14
(C) 19
(D) 25
(E) 30

We want to use as few tennis balls as possible. We know five of the buckets can be the same.

So we want those five identical buckets to have as few balls as possible. We'll put 1 ball in each.

The other buckets all have to be different. We can't use 1 again, so we have to get bigger But we'll use the smallest integers we can: 2, 3, 4, and 5

Voila, we've minimized the number of balls. Then just add this up, and you're done.

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Re: Tennis Balls are to be placed in nine buckets  [#permalink]

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06 Oct 2018, 07:31
fameatop wrote:
Tennis balls are to be placed into 9 buckets so that each bucket contains at least one ball, at the request of detail- oriented players. At most, five of the buckets are to contain the same number of balls, and no two of the remaining buckets are to contain an equal number of balls. What is the least possible number of balls needed for the buckets?
A)8
B)14
C)19
D)25
E)30

To minimize the number of tennis balls used, we should maximize the number of buckets that contain 1 ball.

The question says that at most 5 buckets contain the same number of balls; this means that we can have five buckets with 1 ball each.

The remaining buckets must have unique numbers of tennis balls; since we’re looking for the minimum total number, let’s use 2, 3, 4, and 5.

This gives us a total of 19 tennis balls in the 9 buckets, so C is correct.
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Re: Tennis Balls are to be placed in nine buckets   [#permalink] 06 Oct 2018, 07:31
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