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# What is the least number of marbles required to fill 7 holes so that

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What is the least number of marbles required to fill 7 holes so that  [#permalink]

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07 Apr 2017, 06:48
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

75% (00:52) correct 25% (01:01) wrong based on 68 sessions

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What is the least number of marbles required to fill 7 holes so that no adjacent holes have the same number of marbles and no hole is left empty?

A. 7
B. 10
C. 11
D. 12
E. 28

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Joined: 11 Sep 2015
Posts: 3447
Location: Canada
Re: What is the least number of marbles required to fill 7 holes so that  [#permalink]

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07 Apr 2017, 06:54
1
Top Contributor
Bunuel wrote:
What is the least number of marbles required to fill 7 holes so that no adjacent holes have the same number of marbles and no hole is left empty?

A. 7
B. 10
C. 11
D. 12
E. 28

no hole is left empty
So, let's start by placing 1 marble in each hole.
We get: 1 1 1 1 1 1 1 (7 balls so far, but this breaks the other rule...)

no adjacent holes have the same number of marbles
Let's add an extra marble to every second hole.
We get: 1 2 1 2 1 2 1

This satisfies both rules.
1 + 2 + 1 + 2 + 1 + 2 + 1 = 10

Answer:

Cheers,
Brent
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Re: What is the least number of marbles required to fill 7 holes so that  [#permalink]

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07 Apr 2017, 07:15
answer is B

10

1+2+1+2+1+2+1
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Re: What is the least number of marbles required to fill 7 holes so that  [#permalink]

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28 Jan 2019, 09:13
Bunuel wrote:
What is the least number of marbles required to fill 7 holes so that no adjacent holes have the same number of marbles and no hole is left empty?

A. 7
B. 10
C. 11
D. 12
E. 28

1,2,1,2,1,2,1
=sum all
=> 10
IMO B
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Re: What is the least number of marbles required to fill 7 holes so that   [#permalink] 28 Jan 2019, 09:13
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# What is the least number of marbles required to fill 7 holes so that

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