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Welcome to the PuzzleUp; a problem and games site where each week a different problem is put accross for you to think on and try to solve.

The fundamental aim of this site is to support and raise persons of the information age who have highly developed capabilities of thinking, perceiving and problem solving and who are able to interpret different cultures and contribute to contemporary civilisation.

To keep us on track and give us direction we look forward to hearing your criticisms and suggestions.

Hoping that wisdom, peace and love will master the future of the world we live in.

Emrehan Halici

No: 12       October 17, 2018



12 people sit on a round table to play a variation of the telephone game. They are numbered from 1 to 12 in clockwise order, i.e. the people with adjacent numbers (including 1 and 12) sit next to each other. Person #1 chooses a secret word and starts the game by randomly selecting one of the two neighbors and whispering the word to that person. Upon hearing the word, each person continues the game by randomly selecting one of the neighbors and whispering the word. The game ends when everyone knows the secret word.

What is the probability that the last person whispering the word is numbered 6?

Enter your answer as a reduced fraction. Example: 123/4567

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before you can submit an answer ]

Today's Bonus: 0 point
Popularity: 86.4 %     Difficulty: 81.8 %    

1.TURKEY Seluk Kumbasar897
1.BELGIUM Chia-tche Chang897
1.FRANCE Pierre Forest897
1.FRANCE Romon Christian897
1.RUSSIAN FEDERATION Dmitry Litvinenko897
1.NEW ZEALAND Stephen Merriman897
1.UNITED STATES Mark Rickert897
1.FRANCE Redyellow Jp897
1.UNITED STATES Clive Dawson897
[ Score Table ]
1. DICE GAME 93.8
5. SCALE 75.0
10. CARDS 50.0
[ All Puzzles ]
Comments Add a Comment

Do i have to connect a tree to every other tree with a cord?

Mauricio Mikola - October 10, 2018 - 12:21
   [SCALE] Ouch...

This question will break a lot of egos... i can soo hear the shatters. I was waiting this particular type of question to expand for quite some time.

zugzwang - October 03, 2018 - 17:57

Dear PuzzleUp Contenders,

To clarify the meaning, the question text has been changed.

Old: "...numbers add up to… "

New: "...positive integers add up to… "

Please take notice and submit your answers accordingly.

The PuzzleUp Team

PUZZLEUP - September 20, 2018 - 10:11

Are the randomly chosen questions for the scoreboard the same questions for everybody or are they random too? Thanks

laydogan - September 19, 2018 - 15:27

Randomly chosen problems are the same for every competitor.

PuzzleUp Team [Administrator] - September 20, 2018 - 10:29
   [LARGEST MULTIPLICATION] Only positive or as well negative?

Are we talking about only positive numbers or are negative numbers included as well?

zibelas - September 19, 2018 - 11:56
   [LARGEST MULTIPLICATION] Clarification needed

Are they positive integers?

laydogan - September 19, 2018 - 11:38
   [DICE GAME] "Expected value"...

@ Özcan T:
The "expected value" (mathematical concept of the field of probabilities) of the result of a single throw of one fair 6-sided die is (1+2+3+4+5+6)/6 = 21/6 = 7/2 which IS a fraction.

Puzlifouk - September 19, 2018 - 10:49

Sorry but in this question I am not sure what we are asked to calculate.. Looks like a statement or a part missing.. How can the expected value of points be a fraction?

Özcan T - September 12, 2018 - 17:51
   [NUMBER SELECTION] Explanation : divisibility by 2

To those who do not understand the question of "Number selection", I would only explain - if it is allowed - the solution for divisibility by 2.
Of all three numbers, there are always some: at least two that are even, or at least two that are odd. By adding these two numbers (the two even or the two odd) we can always find Y = 2 numbers taken from X = 3 whose sum is divisible by 2.
If X = 2, this is no longer possible. Counter-example if Y = 1: 3 and 15. It is not possible to select 1 number divisible by 2, since the two proposed are odd.
Counter-example if Y = 2:
3 and 8; it is not possible to select 2 numbers whose sum is divisible by 2, since the only possible choice is 3 + 8 = 11.

Puzlifouk - September 05, 2018 - 05:01
   [NUMBER SELECTION] My explanation

They select any X integers. You select Y of them as you wish. Sum of them (Y integers) will be divisible by 7. Find the minimum number X and Y that guarantees that requirement.

laydogan - September 04, 2018 - 11:29
   [NUMBER SELECTION] I think I get it now

The question should read something like “Given any X integers (not necessarily distinct), if it is always *at least one way* possible to select Y of them whose sum is divisible by 7, what is the minimum value of X and the corresponding value of Y?”

mark_ - September 03, 2018 - 19:34
   [NUMBER SELECTION] Can anyone?

Can anyone who understands the question speak to those who can not (like me)?

Enormous - September 01, 2018 - 23:34
   [NUMBER SELECTION] Impossible Question

This problem is paradoxical there is no right answer. If we are looking for a case where the X integers must be allowed to be any integers then we will be able to find counter examples as in other comments. If I’m the other hand we are only looking for a single case which makes this true then the answer will always be 11. To follow the example for divisibility by 2. Picking the internet of 2 then X = 1 and Y would also select the only value possible.

mark_ - September 01, 2018 - 05:37

I misunderstood the text, thats okay.

kartalwolf - August 31, 2018 - 15:42

It took me all day to understand this puzzle, but the proof that I had the right answer was easy. I congratulate you on posing this elegant puzzle!

Bob Henderson - August 31, 2018 - 02:07
   [NUMBER SELECTION] Objection to the text

When we have two numbers,
even even or even odd or odd odd
Two numbers are enough to select numbers whose sum divisible by 2
For ex
3, 5 here Y=2
Or 3,4 in this case y=1
So x is 2 and Y should be 2
Would you please clarify the text?

kartalwolf - August 30, 2018 - 06:44
   [NUMBER SELECTION] Answer format

"Enter the minimum X, then the corresponding Y without using a space in between."

Does that mean that X and Y must be concatenated, i.e., enter "32" if X=3 and Y=2 for the example?

Because usually we are required to put a "," between the two values.

cchang - August 29, 2018 - 18:03

The answer would be 32.

PuzzleUp Team [Administrator] - August 30, 2018 - 08:34
   About number selection

Sorry but I could not understand the question exactly

Enormous - August 29, 2018 - 14:56
   [NUMBER SELECTION] How to enter the result?

"Enter the minimum X, then the corresponding Y without using a space in between."

In the example where X=3 and Y=2, would that be "32"? Or "3,2"?

Turzz - August 29, 2018 - 12:25

The answer would be 32.

PuzzleUp Team [Administrator] - August 30, 2018 - 08:35

if numbers are 1,2,3 then, when chosen 1,2 as given 2, the sum is not divisible by 2. how possible?

kartalwolf - August 29, 2018 - 12:16

For the example, X=2, Y=2 (both Integers 1) is possible to divide by 2. Since the two numbers are smaller, where is the error?

zibelas - August 29, 2018 - 12:10

How is difficulty calculated. I assume a high difficulty means it is harder, correct?

mark_ - August 23, 2018 - 03:54

Dear PuzzleUp Contenders,

For clarification, a line has been added to the example:

(1+2+3+4+5+6+7+8+9+ 1+0+ 1+1+ 1+2+ 1+3+ 1+4+ 1+5+ 1+6+ 1+7+ 1+8 =90)

Please take notice and submit your answers accordingly.

The PuzzleUp Team

PUZZLEUP - August 22, 2018 - 18:41
   about My Answers

If my answer is correct at the first time , will the My Answers sheets show 100 points or 0 points immediately?

willzhang - August 03, 2018 - 00:35

It will swow 0 points.
Rule 8. The scoreboard is updated approximately once a month. The points on the scoreboard correspond to correct answers for randomly chosen problems and include bonus points. (The number of randomly chosen problems is equal to half of the total number of problems).

PuzzleUp Team [Administrator] - August 03, 2018 - 10:33

Dear PuzzleUp Contenders,

To clarify the meaning, a note has been added:

Note: Each shape must have an area greater than zero.

Please take notice and submit your answers accordingly.

The PuzzleUp Team

PUZZLEUP - August 02, 2018 - 08:26

Dear PuzzleUp Contenders,

To clarify the meaning, the question text has been changed.

Old: "...and a rectangle with distinct side lengths..."

New: "...and a rectangle which is not a square..."

Please take notice and submit your answers accordingly.

The PuzzleUp Team

PUZZLEUP - August 01, 2018 - 15:27
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