Sum of Geometric Progression

Logic Level 4

I have 6 bags, each bag contains a non-zero amount of marbles such that:

the 2nd bag contains twice as many marbles as the 1st bag,
the 3rd bag contains twice as many marbles as the 2nd bag,
the 4th bag contains twice as many marbles as the 3rd bag,
the 5th bag contains twice as many marbles as the 4th bag,
the 6th bag contains twice as many marbles as the 5th bag.

What is the minimum total number of marbles used in these 6 bags?

Image Credit: Flickr Swede-Heart .

The answer is 32.

1 solution

Pi Han Goh
Jul 7, 2015

Moderator note:

That's tricky. I didn't expect to put bags within bags.

Haha... @Pi Han Goh ...I like that! I just kept wondering why the answer isn't 63...love it!! Do keep more of such problems coming!!!

Noel Lo - 5 years, 11 months ago

Whoa nice one. I put $63$ at first, took me several minutes to see the solution. :)

Alex Li - 5 years, 11 months ago

Narrative of the question was misleading

Ashok Aggarwal - 5 years, 11 months ago

The phrasing was misleading to the extent that I'd say an answer of 32 is based on a huge assumption. Nothing in the question suggests that the narrative is bags within bags. Might wanna make that clearer for future problems. =)

That aside, nice question! Would have been great to attempt!

Thevesh Theva - 5 years, 11 months ago

I sort of agree with you. Some fool who does not know how to compute a simple geometric progression (and who did not read the problem well) might have answered 32 purely because that is what he expects the 6th bag to contain. I almost guessed 32 myself just because I was frustrated that my answer was rejected, but decided not to because my guesswork counts for nothing in the real world. Maybe this problem should be located in the logic section (though that might, unfortunately, give the answer away).

Jared Jones - 5 years, 11 months ago

That was highly unexpected.

Paul Paul - 5 years, 11 months ago

It says a non-zero amount. You could start with negative infinity.

Rory Collins - 5 years, 11 months ago

you cannot have negative no. of marbles though !!

Harish Ganesan - 5 years, 10 months ago

But, where is ANY hint of "bag within bag" in the question ???

Murali Nagarajan - 5 years, 10 months ago

Oh, so each bag is inside the other?

Vishnu Bhagyanath - 5 years, 11 months ago

Yep, just like Matryoshka doll.

Pi Han Goh - 5 years, 11 months ago

This solution made my day :)

Trung Đặng Đoàn Đức - 5 years, 11 months ago

Similar Unique method

Vraj Mistry - 5 years, 11 months ago

Thats what I thought of!

Rohit Ner - 5 years, 11 months ago

I don't understand this. Could you please explain?

Ashley Shamidha - 5 years, 11 months ago

Sum of numbers inside each ellipse represents the number of marbles in each respective bags.

Pi Han Goh - 5 years, 11 months ago

Interesting problem!!

Ashley Shamidha - 5 years, 11 months ago

Whoaa...are you kidding me...too great man, hats off to you....

Abhay Tiwari - 5 years, 11 months ago

EXCELLENT!! Unexpected

Niraj Upadhyay - 5 years, 11 months ago

First I thought 63, then i saw the rating of the problem which was 80points at the time and no problem would be rated that high if it was so simple. So i thought for a while and figured it out.

Rahul Badenkal - 5 years, 11 months ago

Hats off Pi Han Goh I thought it was 63

Riddhesh Deshmukh - 5 years, 8 months ago

It was indeed a brilliant problem!!

Saish Thakur - 1 year, 4 months ago

Sum of Geometric Progression

Image Credit: Flickr Swede-Heart .

The answer is 32.

1 solution

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