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

Emrehan Halici



No: 19       December 05, 2018


CLOSED AREAS

CLOSED AREAS

A 2x2 digital display consists of 12 segments. You will create a shape by turning some of the segments on. Rules:

• At least one of the segments will be on.
• Turned on segments will create one or more closed area.
• Each turned on segment will be on the perimeter of a closed area.

How many different shapes can be created?

For example: for a 1x2 digital display with 7 segments the answer would be 4.
2 shapes with 1 square, 1 shape with 2 squares and 1 shape with a rectangle.

[ You need to be a member of this site
before you can submit an answer ]

Today's Bonus: 1 point
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Popularity: 42.9 %     Difficulty: 18.8 %    

1.UNITED STATES Clive Dawson1317
1.FRANCE Redyellow Jp1317
1.NEW ZEALAND Stephen Merriman1317
1.FRANCE Romon Christian1317
1.TURKEY Seluk Kumbasar1317
1.BELGIUM Chia-tche Chang1317
1.RUSSIAN FEDERATION Dmitry Litvinenko1317
1.GERMANY Gabi Penn-karras1317
1.ITALY Jean Manuel Morales1317
1.UNITED STATES Mark Rickert1317
[ Score Table ]
1. DICE GAME 93.8
2. THE TELEPHONE GAME 86.4
3. NUMBER SELECTION 83.3
4. RECTANGLES 80.6
5. CORDED TRIANGLES 79.2
6. SCALE 75.0
7. TRIANGLE, SQUARE, RECTANGLE 75.0
8. LARGEST MULTIPLICATION 70.0
9. DIGITAL DISPLAY 56.3
10. PRIME NUMBER 55.0
[ All Puzzles ]
Comments Add a Comment
   [PRIME NUMBER] 1

Do you consider 1 to be prime?

kublai - November 28, 2018 - 19:15
   [RECTANGLES] Cotation and advice

Hello,
I really like this problem, quite pure, but whose resolution is not quite basic. For the clarification, however, I would have rather phrased it as follows: "The large rectangle may be a square, or not, and one of its side may have the same length as one side of one of the small rectangles".

Puzlifouk - November 15, 2018 - 12:30
   NOTE

Dear PuzzleUp Contenders,

To clarify the meaning, a note has been added:

“Note:The large rectange can not be a square.”

Please take notice and submit your answers accordingly.

Regards,
The PuzzleUp Team

PUZZLEUP - November 15, 2018 - 12:14
   [DIFFERENT DIGITS] digits meaning

if number is 3568
in this number 5 means: five or five hundred??

cem uzun - November 01, 2018 - 10:55
   [DIFFERENT DIGITS] Clarification

Dear PuzzleUp Contenders,

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

Old: "... each of its digits … "

New: "... each of its digits (except the leftmost digit) … "

Please take notice and submit your answers accordingly.

Regards,
The PuzzleUp Team

PUZZLEUP - November 01, 2018 - 06:23
   [CORDED TRIANGLES] Doubt

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
   [LARGEST MULTIPLICATION] Ammendement

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.

Regards,
The PuzzleUp Team

PUZZLEUP - September 20, 2018 - 10:11
   Scoreboard

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
   [DICE GAME]

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.
QED

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
   [NUMBER SELECTION] Sorry

I misunderstood the text, thats okay.

kartalwolf - August 31, 2018 - 15:42
   [NUMBER SELECTION]

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
   [NUMBER SELECTION]

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
   [NUMBER SELECTION]

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
   Difficulty

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

mark_ - August 23, 2018 - 03:54
   [DIGIT SUMS] CLARIFICATION

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.

Regards,
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
   [TRIANGLE, SQUARE, RECTANGLE] NOTE

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.

Regards,
The PuzzleUp Team

PUZZLEUP - August 02, 2018 - 08:26
   [TRIANGLE, SQUARE, RECTANGLE] Amendment

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.

Regards,
The PuzzleUp Team

PUZZLEUP - August 01, 2018 - 15:27
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