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Tamari




 
 
 
 

Post  Fri, Oct 16 2020, 2:58 pm
Solution for 50 coins riddle:
Hidden: 

It’s really very simple. Before starting the game, player A adds up all coins in odd positions, and all coins in even positions, and sees whichever total is greater.
Since there’s an even number of coins, he can always make sure to take coins on a specific (odd/even) position.
For instance, say odd ones are greater. On first play, he has choice of coin #1 or #50. By choosing 1, player B has to choose between #2 and #50, thereby exposing an odd one no matter which one he chooses. And so the pattern continues...
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ExtraCredit




 
 
 
 

Post  Fri, Oct 16 2020, 3:20 pm
Tamari wrote:
Solution for 50 coins riddle:
Hidden: 

It’s really very simple. Before starting the game, player A adds up all coins in odd positions, and all coins in even positions, and sees whichever total is greater.
Since there’s an even number of coins, he can always make sure to take coins on a specific (odd/even) position.
For instance, say odd ones are greater. On first play, he has choice of coin #1 or #50. By choosing 1, player B has to choose between #2 and #50, thereby exposing an odd one no matter which one he chooses. And so the pattern continues...

So simple Banging head
If you notice, my first answer did go in the even odd direction but I couldn’t figure it out all the way. Good one!
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tothepoint




 
 
 
 

Post  Fri, Oct 16 2020, 3:47 pm
What makes this number unique: 8,549,176,320?
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ChanieMommy




 
 
 
 

Post  Sat, Oct 17 2020, 2:02 pm
Tamari wrote:
2 friends decide to play a game. They arrange 50 coins in a line on the table, with various nominations. Then, alternating, each player takes on their turn one of the two coins at the ends of the line and keeps it. They continue doing this, until after the 50th move all coins are taken. Prove that whoever starts first can always collect coins with at least as much value as their opponent.


Here is the winning strategy.
Hidden: 

Let's assign the coins numbers from 1 to 50.
Tally the worth of the coins which have odd numbers.
Tally the worth of the coins which have even numbers.
If the odd coins are worth more, take coin nr. 1.
If the even coins are worth more, take coin nr. 50.
If they are worth the same, take either (or develop a strategy that maximises your gains by switching, but this is not always possible it will depend on the situation).

From then on, always take coins from the same side as your opponent.
This way, you will collect at least as much as him.

In some situations, you can maximise your gains by switching from odd to even or vice-versa, but this has to be done carefully it could also lead you to loose the game...

Since there is an even number off coins in the beginning, you are free to choose whether you want odd or even. Your adversary, however, will not be able to choose...

If you take away nr. 50, he can either take 1 or 49, both odd.
If you take away nr. 1 he can either take 2 or 50, both even.

If you then always take from the same end as him, he will be constrained to always stay with the oddd (or even) numbers...

He will not be able to switch from odd to even or vice-versa, unless you switch him, by not taking from the same end as him...
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ChanieMommy




 
 
 
 

Post  Sat, Oct 17 2020, 2:05 pm
tothepoint wrote:
What makes this number unique: 8,549,176,320?


Hidden: 

It contains figures 0 through 9 and...????
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doodlesmom




 
 
 
 

Post  Sat, Oct 17 2020, 7:51 pm
ChanieMommy wrote:
Hidden: 

It contains figures 0 through 9 and...????


There must be more to it...
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ExtraCredit




 
 
 
 

Post  Sat, Oct 17 2020, 8:02 pm
tothepoint wrote:
What makes this number unique: 8,549,176,320?
Hidden: 


549,176,320 is a multiple of the first digit 8
As is every column separately549,000,000 is a multiple of 8
176,000 is a multiple of 8, and 320 is too. Plus all digits are different. So this number is pretty unique but I wonder if this is the answer you’re looking for.
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ChanieMommy




 
 
 
 

Post  Sat, Oct 17 2020, 8:07 pm
ExtraCredit wrote:
Hidden: 


549,176,320 is a multiple of the first digit 8
As is every column separately549,000,000 is a multiple of 8
176,000 is a multiple of 8, and 320 is too. Plus all digits are different. So this number is pretty unique but I wonder if this is the answer you’re looking for.


Well, 1000 is a multiple of eight (2x2x2x5x5x5), so it's logical that anything that ends in 000 is a multiple of 8...
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ExtraCredit




 
 
 
 

Post  Sat, Oct 17 2020, 8:30 pm
ChanieMommy wrote:
Well, 1000 is a multiple of eight (2x2x2x5x5x5), so it's logical that anything that ends in 000 is a multiple of 8...

Hidden: 

176 and 320 are multiples without the thousands, that’s what made me make the first column work already as well. Plus those 9 digits are a multiple too so you can skip the 1,000 answer. But, all this aside, I’d be surprised if this is the answer she’s looking for. She probably wants “more”
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tothepoint




 
 
 
 

Post  Sat, Oct 17 2020, 9:35 pm
Sorry to get you all worked up ExtraCredit! It’s actually more of a riddle and does not require math nor logic
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ExtraCredit




 
 
 
 

Post  Sat, Oct 17 2020, 9:38 pm
tothepoint wrote:
Sorry to get you all worked up ExtraCredit! It’s actually more of a riddle and does not require math nor logic

Oh that’s easy then
Hidden: 

Alphabetical order
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ExtraCredit




 
 
 
 

Post  Sat, Oct 17 2020, 9:39 pm
Was indeed a waste of brain energy. Should’ve saved it for the next coin riddle. LOL
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Tamari




 
 
 
 

Post  Sat, Oct 17 2020, 10:58 pm
100 mathematicians live on an island, along with the island's leader. 60 have brown eyes, and 40 have blue eyes, but no-one knows his own color. One day, the leader of the island (who has green eyes)made an announcement as follows:
"I can see at least one person with blue eyes. Starting tonight, there will be a plane at 8 pm every night. Whoever discovers they have blue eyes, must leave the island that night."
There are no mirrors on the island, and it is considered to be in very poor taste to discuss the subject of eye color. Of course, everyone knows what everyone else’s eye color is.
What effect did that announcement have? How many people leave the island and when?
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doodlesmom




 
 
 
 

Post  Sun, Oct 18 2020, 12:20 am
Just saying I really enjoyed sharing some of the riddles with my family this weekend.
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ExtraCredit




 
 
 
 

Post  Sun, Oct 18 2020, 12:23 am
Tamari wrote:
100 mathematicians live on an island, along with the island's leader. 60 have brown eyes, and 40 have blue eyes, but no-one knows his own color. One day, the leader of the island (who has green eyes)made an announcement as follows:
"I can see at least one person with blue eyes. Starting tonight, there will be a plane at 8 pm every night. Whoever discovers they have blue eyes, must leave the island that night."
There are no mirrors on the island, and it is considered to be in very poor taste to discuss the subject of eye color. Of course, everyone knows what everyone else’s eye color is.
What effect did that announcement have? How many people leave the island and when?

Dunno in which direction to think
Hidden: 


Why did the leader say he sees at least 1
8 pm is dark. Does that matter?
No mirrors on an island but perhaps they can use the water for a mirror?
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Tamari




 
 
 
 

Post  Sun, Oct 18 2020, 12:27 am
ExtraCredit wrote:
Dunno in which direction to think
Hidden: 


Why did the leader say he sees at least 1
8 pm is dark. Does that matter?
No mirrors on an island but perhaps they can use the water for a mirror?


No tricks here. It is a very hard riddle, though purely logical. The fact that they're all mathematicians, makes this whole riddle possible....
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ExtraCredit




 
 
 
 

Post  Sun, Oct 18 2020, 12:29 am
Tamari wrote:
No tricks here. It is a very hard riddle, though purely logical. The fact that they're all mathematicians, makes this whole riddle possible....

Ready for a hint
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doodlesmom




 
 
 
 

Post  Sun, Oct 18 2020, 12:32 am
Do they want to leave the island? Otherwise as long as they don’t discuss eye color they’re good! Everyone gets to stay- since they don’t know yet that their eye color is blue.
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Tamari




 
 
 
 

Post  Sun, Oct 18 2020, 12:32 am
ExtraCredit wrote:
Ready for a hint

Hidden: 

start by assuming there were only 2 blue-eyes people
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ExtraCredit




 
 
 
 

Post  Sun, Oct 18 2020, 12:35 am
Tamari wrote:
Hidden: 

start by assuming there were only 2 blue-eyes people

Hidden: 

Oh do they know that it’s 60/40?
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