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No: 08       September 19, 2018


LARGEST MULTIPLICATION

LARGEST MULTIPLICATION

A group of positive integers add up to 50 and none of the numbers is divisible by another. What is the maximum possible value of the multiplication of the numbers in this group?

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Popularity: 72.2 %     Difficulty: 30.6 %    

1.UNITED STATES Darren Seneker616
1.TAIWAN, PROVINCE OF CHINA Ping Chuang616
1.NEW ZEALAND Stephen Merriman616
1.RUSSIAN FEDERATION Sergey Shtyka616
1.UNITED STATES Chris Becker616
1.GERMANY Dyballa Matthias616
1.TAIWAN, PROVINCE OF CHINA Acgfans Ptt616
1.TAIWAN, PROVINCE OF CHINA Buffalo Bill Chen616
1.MEXICO Rodrigo Nungaray616
1.INDIA Gaurav Singh616
[ Score Table ]
1. DICE GAME 93.8
2. NUMBER SELECTION 83.3
3. TRIANGLE, SQUARE, RECTANGLE 75.0
4. LARGEST MULTIPLICATION 72.2
5. THREE ORDERS 53.1
6. LETTER COUNT 50.0
7. CARDS 50.0
8. DIGIT SUMS 50.0
9. --
10. --
[ All Puzzles ]
Comments Add a Comment
   [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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