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Marble Mania: Newsletter Challenge (September 2020)

Posted August 31, 2020 5:01 PM
Pathfinder Tags: challenge question marbles

This month's GlobalSpec Newsletter Challenge is:

Can you place 10 marbles in three empty cups so that there is an odd number in each cup?

Hint: there are fifteen different solutions to this problem. You only have to find one!

And the answer is:

All fifteen solutions involve placing one of the cups into another. For example, Cup 1 could contain one marble, Cup 2 could contain two marbles, and the remaining seven marbles could be placed in Cup 3; placing Cup 2 into either Cup 1 or 3 then ensures that there is an odd number in each cup.

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SolarEagle
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#1

Re: Marble Mania: Newsletter Challenge (September 2020)

08/31/2020 6:24 PM

1,1,1..

1,1,3...3,1,1....1,3,1

1,1,5...1,5,1....5,1,1

1,1,7...1,7,1....7,1,1

1,3,5...5,3,1....3,1,5

1,3,3...3,3,1....3,1,3

3,3,3..

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jdretired
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#2

Re: Marble Mania: Newsletter Challenge (September 2020)

08/31/2020 8:06 PM

Can you place all 10 marbles in three empty cups?

Is all correct, or is it a suggestion?

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Rixter
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#3
In reply to #2

Re: Marble Mania: Newsletter Challenge (September 2020)

08/31/2020 8:49 PM

Obviously, you can't use all ten marbles. The sum of 3 odd numbers has to be odd.
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jdretired
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#5
In reply to #3

Re: Marble Mania: Newsletter Challenge (September 2020)

08/31/2020 9:04 PM

Yes I agree with you, it's obvious. Just pointing out that using all the 10 balls, is only a suggestion?

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SolarEagle
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#4
In reply to #2

Re: Marble Mania: Newsletter Challenge (September 2020)

08/31/2020 8:55 PM

I guess if you wanted to cut the 10th marble into thirds and add one third marble to each cup you could...kind of stretching the definition it seems to me....

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#6

Re: Marble Mania: Newsletter Challenge (September 2020)

08/31/2020 9:05 PM

Can you place 10 marbles in three empty cups so that there is an odd number in each cup?

OK, put 1 marble in the first cup and set it aside.

Put 2 marbles in the second cup.

Put 7 marbles in the third cup and put it inside the second cup.

Now, the first cup has 1 marble, the third cup has 7 marbles, and the second cup (with the third cup inside) has 2+7 = 9 marble inside of it.

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SolarEagle
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#7
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Re: Marble Mania: Newsletter Challenge (September 2020)

09/01/2020 6:23 AM

Ahh.... the third cup becomes a Schrodinger's cup...it both exists and doesn't exist at the same time....

I like it!

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SolarEagle
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#16
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Re: Marble Mania: Newsletter Challenge (September 2020)

09/14/2020 6:25 PM

https://www.pedagonet.com/puzzles/tea1.htm

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canadianslidewinder
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#17
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Re: Marble Mania: Newsletter Challenge (September 2020)

09/15/2020 9:17 AM

In the referenced link, the problem is to distribute ten cubes of sugar in three tea cups so that there is an odd number of sugar lumps in each cup. Since these are cubes of sugar and not marbles, as in the CR4 puzzle, and since no time limit is specified to effect the required odd-numbered distribution, and since the distributed odd numbered cubes are described as "lumps" and not cubes, therefore, in strict accordance with this interpretation, the correct "solution" is this: Distribute the ten sugar cubes in the three tea cups in any quantity of your choosing. Add tea to each tea cup sufficient to dissolve the sugar cubes contained therein. Wait for the tea to evaporate. When the tea has evaporated there will be one lump of sugar in the bottom of each cup. One is an odd number, as specified; and in each cup is a lump of sugar (not a cube), also as specified.

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garth
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#22
In reply to #6

Re: Marble Mania: Newsletter Challenge (September 2020)

09/29/2020 9:25 PM

Is that cup or cups?

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Brenda Dean
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#8

Re: Marble Mania: Newsletter Challenge (September 2020)

09/01/2020 9:48 AM

one marble in one cup; nine marbles in the next cup; put the second cup in the third cup.
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Anonymous Poster #1
#9

Re: Marble Mania: Newsletter Challenge (September 2020)

09/01/2020 11:54 AM

Assuming the cups are tapered to allow stacking, the strategy would be to put an even number (or zero) marbles in the first cup, thus allowing you to put an odd number of marbles in the second and third cups. By stacking the second cup into the first, you are adding an odd number of marbles to the even number in the first cup, creating a situation in which all cups have an odd number of marbles in them.

All 15 solutions are shown below (Note: Cup numbers are arbitrary as long as you are stacking an odd marbled cup into the even):

1) Cup 1:0 Cup 2:9 Cup 3:1

2) Cup 1:2 Cup 2:7 Cup 3:1

3) Cup 1:4 Cup 2:5 Cup 3:1

4) Cup 1:6 Cup 2:3 Cup 3:1

5) Cup 1:8 Cup 2:1 Cup 3:1

6) Cup 1:0 Cup 2:7 Cup 3:3

7) Cup 1:2 Cup 2:5 Cup 3:3

8) Cup 1:4 Cup 2:3 Cup 3:3

9) Cup 1:6 Cup 2:1 Cup 3:3

10) Cup 1:0 Cup 2:5 Cup 3:5

11) Cup 1:2 Cup 2:3 Cup 3:5

12) Cup 1:4 Cup 2:1 Cup 3:5

13) Cup 1:0 Cup 2:3 Cup 3:7

14) Cup 1:2 Cup 2:1 Cup 3:7

15) Cup 1:0 Cup 2:9 Cup 3:1
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jmueller
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#10
In reply to #9

Re: Marble Mania: Newsletter Challenge (September 2020)

09/01/2020 10:24 PM

Your 15 answers are very good, but #15 has the contents of cups 2 & 3 reversed. As stated, it is a duplicate of the first answer. I suspect a simple "typo" as you were making your post.

--JMM
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rashavarek
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#11

Re: Marble Mania: Newsletter Challenge (September 2020)

09/02/2020 11:10 AM

But why stop there? r

Or maybe you're a bit older...

This was one wicked game.

Or perhaps you qualify as antique.

Marble mania takes many forms.

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HiTekRedNek
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#19
In reply to #11

Re: Marble Mania: Newsletter Challenge (September 2020)

09/29/2020 10:17 AM

I am old fashioned.Marbles were the Android Phone of the '50's and "60's.I had a spherical groove in my thumb nail,worn down to fit the marbles.

Players could put "English" ("spin") on a marble to make it curve,like a bowler does.

You had certain marbles that were"stickers" that would stay in the circle while knocking others out.You had "Busters" that were a larger one used to break up the first shot.Steel ones that would break the marbles into sharp shards and you were not allowed to remove them,you had to play around them.Lag to the line to see who shoots first;circles,triangles,star shaped rings,variations were unlimited.

Marbles were currency,traded for everything like Twinkies,BB's,fire crackers,caps for cap pistols,deputy badges,but you never traded a good sticker or buster.

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rashavarek
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#20
In reply to #19

Re: Marble Mania: Newsletter Challenge (September 2020)

09/29/2020 10:24 AM

You and me both. I still have my "hive" of bumble bees. ;-)

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canadianslidewinder
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#21
In reply to #19

Re: Marble Mania: Newsletter Challenge (September 2020)

09/29/2020 10:49 AM

In the same era, we played marbles here in Southern Ontario, but we also had another game employing chestnuts, which I'm not sure was unique to this area. A hole was drilled through the centre of a chestnut and a shoelace was then threaded through the hole and the chestnut held in place by a stopper knot at the end of the shoelace. The point was to attempt to smash the other guy's chestnut by swinging yours down upon his while he held his suspended in front of him. A "kill" was declared only if the chestnut was busted off the shoelace. A chunk could be knocked off the side, but as long as it was still on the shoelace, the chestnut was still "alive". After your swing, whether you hit or missed, it was then his turn, and so on. Your chestnut gained a "life" for every other chestnut it smashed and killed. Also, if it smashed, for example, an opponent's "five life" chestnut, those five lives would be added to yours. There were various recipes and preparations (some secret or only shared with close friends) to make a chestnut both hard and tough. Soaking overnight in vinegar and then baking in the oven was one purported method.

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Randall
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#25
In reply to #21

Re: Marble Mania: Newsletter Challenge (September 2020)

11/28/2020 11:06 AM

Are you sure you were using chestnuts, not horse chestnuts AKA conkers

Many years ago one of my friends who happened to be a headmaster got caught cheating with a conker filled with concrete in our local pubs anual conker competion. It made the national news. What very few people knew was that the guy who won had filled his with epoxy.

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canadianslidewinder
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#26
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Re: Marble Mania: Newsletter Challenge (September 2020)

11/28/2020 12:33 PM

You are correct. Here in S. Ontario it is horse chestnuts. Not a common tree but there was one growing in the front yard of a house on the way to school. In the fall when the nuts were ripe the lady owner had trouble keeping the kids out of her tree. I read that the conker game originated in the UK. In those days inhabitants of Peterborough, Ontario were probably 98% British, Scottish, Irish origin, so our parents and grandparents brought the game with them to the New World. Filling the nut with epoxy - great idea!

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canadianslidewinder
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#12

Re: Marble Mania: Newsletter Challenge (September 2020)

09/02/2020 7:06 PM

Note that the question is "... so that there is an odd number in each cup?" not so that there is an odd number of marbles in each cup. Therefore, with a marker, write a 3, a 5, and a 7 on three different marbles and put those odd numbered marked marbles separately into each of the three cups, then distribute the remaining marbles into the cups in any quantity of your choosing. When done, an "odd number" will indisputably be in each cup.

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MR. Guest
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#13

Re: Marble Mania: Newsletter Challenge (September 2020)

09/04/2020 11:45 AM

If you put, say, five marbles in each of the first two cups, and leave the third cup empty, then the total marbles in the three cups can be ten.

The total of any two positive odd numbers of marbles must be an even number.

The sum of adding a third odd number to that first sum must also be an odd number, which can not total 10...

Assuming, that is, that negative numbers of marbles are not allowed...

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#14

Re: Marble Mania: Newsletter Challenge (September 2020)

09/06/2020 12:45 PM

The answer to the question is a "yes" or "no",not the distribution of the marbles.

A simple question if you do not read anything extra into it.

I cannot do it,so the answer is :"NO"

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canadianslidewinder
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#15
In reply to #14

Re: Marble Mania: Newsletter Challenge (September 2020)

09/06/2020 2:56 PM

And for the "fifteen different solutions" you could say no in fifteen different languages - non, niet, nein ...

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Jedo
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#18

Re: Marble Mania: Newsletter Challenge (September 2020)

09/29/2020 8:18 AM

Simple... place one of the cups inside the other. Then put 5 marbles in the stacked cups and 5 in the remaining cup. All 3 cups have an odd number of marbles in them at that point.
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MR. Guest
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#23

Re: Marble Mania: Newsletter Challenge (September 2020)

10/01/2020 11:13 AM

In response to the ''Answer'' provided, just exactly how is ''... Cup 2 would contain two marbles, ...'' an odd number?... (i.e.: cup 2 still contains an even number of marbles... even after it is placed in another cup... )

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marco bähler
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#24

Re: Marble Mania: Newsletter Challenge (September 2020)

10/15/2020 12:10 AM

i would proceed like this with one of the cups:put three spheres on the table, cover them with the cup, and put one sphere on top of it. so there is an odd number IN the cup and the remaining sphere ON the cup.

whatcha think of this solution?
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