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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.

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Emrehan Halici

No: 07       September 12, 2018



You will play a game with a fair 6-sided die. You will throw the die and as long as the result of the throw is greater than or equal to the previous throw, you will continue throwing. If the throw is lower than the previous one, you will stop and get as many points as the sum of all throws, including the last one. For example, if you get 2, 5, 5, and 3 as a result of 4 throws, the game will end with 15 points.

What is the expected value of the points you will get at the end of the game?

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: 92.9 %     Difficulty: 67.9 %    

1.GERMANY Dyballa Matthias505
1.MEXICO Rodrigo Nungaray505
1.GERMANY Michael Niermann…505
1.UNITED STATES Mark Rickert505
1.CHINA Lugionline Lugio…505
1.TAIWAN, PROVINCE OF CHINA Buffalo Bill Chen505
1.ROMANIA Emil Martinas505
1.FRANCE Raffy Luc505
1.BELGIUM Chia-tche Chang505
[ Score Table ]
1. DICE GAME 92.9
6. CARDS 50.0
7. DIGIT SUMS 50.0
8. --
9. --
10. --
[ All Puzzles ]
Comments Add a Comment

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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