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help 7 years 11 months ago #485475

X + X + X = 30

You can use 1,3,5,7,9,11,13,15
You can also repeat the numbers. help me zarp :zarp:
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help 7 years 11 months ago #485476

There is no solution to this question using normal methods, as three odd numbers added together will always produce an odd number ( Is it possible for an odd number of odd numbers to be added together to create an even number? ). Since the answer is even, and an odd number can not equal an even number, this is unsolvable.


Using trick solutions;

Use the factorial function in your answer: 11 + 3! (1*2*3, which equals 6) + 13 = 30
Change the mathematical base system of the equation in certain places (this can give an answer with multiple bases or a single base): For single bases: ..For multiple bases... 910+910+910=309910+910+910=309. A number which appears as "30" when written in a different base system doesn't represent "thirty" in base ten.

When written in base 9 as 309309, is equivalent to twenty seven in base ten: (27102710).
Or using all the same base: 135+115+15=305135+115+15=305 in base five, which is equivalent to (810+610+110=1510)(810+610+110=1510) in base ten. Or 139+159+19=309139+159+19=309 in base nine.

Use the commas given in the question to your advantage: In many countries the comma (,) is used instead of the full stop (.) to represent a decimal point. For example "3.5" (three and a half) can be written as "3,5". This allows for the solution 11,3 + 15,7 + 3 = 30.
Only use numbers in two of the brackets: You could leave one of the brackets blank and have the answer as () + (15) + (15) = 30. The first fifteen represents a fifteen with a "unary plus" (+15) and the second fifteen added to the first one gives us thirty. The first bracket is left empty.

Rotate one of the accepted numbers so that it resembles a different number: If the number 9 is rotated 180 degrees then it can resemble the number 6. 6 (an upside down number "9") + 9 + 15 = 30.


The five solutions in this section are trick solutions, answering in a similar way to how you would answer a riddle. If you want to have three odd numbers which when added together produce an even number, there are no solutions.
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Last Edit: 7 years 11 months ago by RedPowder.
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help 7 years 11 months ago #485477

Firstly I will show you it is not possible by direct sum, then I’ll demonstrate the different ways to do so.

ANSWER:- Not Possible by direct sum in base 10, because

If you take the numbers to be modulo 2, five odd numbers would sum up to 1, but 30 is 0 modulo 2

WHY:-
Prerequisites:- Knowledge of basic Mathematics.

Number’s are odd numbers

1=2*0+1
3=2*1+1
5=2*2+1
.
.
.
13= 2*6+1
15= 2*7+1
Or we can say that 2*n+1 is an odd number
Now
we can say that the number we have to prove

To prove:- x+y+z=30

For all x,y,z ∈ 2n+1 where n∈N(Natural numbers).
Proof:-here’s no combination. It’s impossible. Every number in that list is odd.

We know that any even number can be expressed as 2n where n is an integer. Any odd number can be expressed as 2n−1.

Let m, n, and k all be integers. Then the sum of three odd numbers can be written as:
(2m−1)+(2n−1)+(2k−1)
=2(m+n+k−1)−1.
Note that m+n+k−1 is another integer. If we call it N then the result is simply
2N−1
which, as we know is an odd number. Therefore the sum of three odd numbers is always an odd number.

Hence Proved.

In simple words, there do not have any odd numbers, where by adding any 3 of them we get 30 because

odd + odd + odd
= (odd + odd) + odd
= even + odd
= odd (and 30 is even number)
Example:-

Let the number is 15,13 and 3 then
15=2*7+1
13=2*6+1
3=2*1+1
where 1,6 and 7
now
15+13+3=2*7+1+2*6+1+281+11
=2(7+6+1)+3
=2*14+3(24 is our 'm')
and 2*14≠30.
OR
15+13+3≠30.
CONCLUSION:- So by adding 3 odd numbers, we do not get 30. Is there any other way to do so?
Yes… Read below..

2.) How Possible:-

With using any function within an operator
How Possible?:-

Factorial method:-
3!+11+13=30
3!+9+15=30
3!+3!+3!+3!+3!=30
11+1+3!+3!+3!=30
5+7+3!+3!+3!=30
11+7+3!+3!+3!=30
3+5+7+9+3!=30
1+5+7+11+3!=30
1+1+3!+11+13=30
1+3+5+3!+15=30 and many more.
Click here to Learn How to find Factorial of a program (Mirror Link)
Changing Base method :-
[(3) + (3) + (3) + (3) + (3)] 5= [(6)+(6)+(6)+(6)+(6)]10= [30]10

(1)7+(5)7+(5)7+(5)7+(5)7=(30)710 + 10 + 10 = 30 in any odd base (seven, nine, eleven, and so on).
Click here to learn_base_conversion (Mirror Link)

Addition-Subtraction Method:-
a+b+c=a+b+(x-y) where x-y=c
15+(13-11)+(9+7-5+3-1)=30
15+(13-11)+(9+7-3)=30
15+(13-9)+(7+3+1)=30
15+(13-9)+(7+5-1)=30
15+(13-7)+(5+3+1)=30
15+13+(3-1)=30
15+13+(5-3)=30
15+13+(7-5)=30
15+13+(9-7)=30
15+13+(9-5-3+1)=30
15+13+(11-9-7+5+3-1)=30
15+13+(11-9 )=30
15+13+(11-9+7-5-3+1)=30
15+13+(11-7-5+3)=30
15+13+(11-7-3+1)=30
15+13+(11-5-3-1)=30
OTHER METHOD
1) 30 cm=(15 cm+13 cm)+ 1cm +(7 mm+3mm)
2)( 1+3)+(13+7) +6 (inverting 9 using mirror ) = 30
3) 11.3 + 15.7 + 3 = 30 (Using decimal)
4) 30 years = 15 years + 13 years + 1 year + 7 months + 5 months(USING Calendar Mathematics)
5) ((13+11)/3) + 1 + 5 + 7 + 9 = 30 (using numbers 1, 3, 5, 7, 9, 11, 13)
6) 3 weeks + 1 Day + 7 Days + 13 Hours + 11 Hours = 30 days (USING Calendar Mathematics)
7) (9/3)+(15/5)+(13+1/7)+(11)+(11)=30 (Using Division Operator)
=>3+3+2+11+11=30
Commas were used instead of decimal points in the past history by Arabs and even in France. You will be surprised to hear that even today in some parts of the world. Commas are written instead of decimal unit or a dot!Using commas in place of decimal units we can easily come up with a solution equal to 30!For example:
13,7 + 15,3 + 1 = 30 !
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help 7 years 11 months ago #485478

RedPowder wrote:
There is no solution to this question using normal methods, as three odd numbers added together will always produce an odd number ( Is it possible for an odd number of odd numbers to be added together to create an even number? ). Since the answer is even, and an odd number can not equal an even number, this is unsolvable.


Using trick solutions;

Use the factorial function in your answer: 11 + 3! (1*2*3, which equals 6) + 13 = 30
Change the mathematical base system of the equation in certain places (this can give an answer with multiple bases or a single base): For single bases: ..For multiple bases... 910+910+910=309910+910+910=309. A number which appears as "30" when written in a different base system doesn't represent "thirty" in base ten.

When written in base 9 as 309309, is equivalent to twenty seven in base ten: (27102710).
Or using all the same base: 135+115+15=305135+115+15=305 in base five, which is equivalent to (810+610+110=1510)(810+610+110=1510) in base ten. Or 139+159+19=309139+159+19=309 in base nine.

Use the commas given in the question to your advantage: In many countries the comma (,) is used instead of the full stop (.) to represent a decimal point. For example "3.5" (three and a half) can be written as "3,5". This allows for the solution 11,3 + 15,7 + 3 = 30.
Only use numbers in two of the brackets: You could leave one of the brackets blank and have the answer as () + (15) + (15) = 30. The first fifteen represents a fifteen with a "unary plus" (+15) and the second fifteen added to the first one gives us thirty. The first bracket is left empty.

Rotate one of the accepted numbers so that it resembles a different number: If the number 9 is rotated 180 degrees then it can resemble the number 6. 6 (an upside down number "9") + 9 + 15 = 30.


The five solutions in this section are trick solutions, answering in a similar way to how you would answer a riddle. If you want to have three odd numbers which when added together produce an even number, there are no solutions.

Holy shit. wow
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help 7 years 11 months ago #485481

joshuaharry wrote:
Firstly I will show you it is not possible by direct sum, then I’ll demonstrate the different ways to do so.

ANSWER:- Not Possible by direct sum in base 10, because

If you take the numbers to be modulo 2, five odd numbers would sum up to 1, but 30 is 0 modulo 2

WHY:-
Prerequisites:- Knowledge of basic Mathematics.

Number’s are odd numbers

1=2*0+1
3=2*1+1
5=2*2+1
.
.
.
13= 2*6+1
15= 2*7+1
Or we can say that 2*n+1 is an odd number
Now
we can say that the number we have to prove

To prove:- x+y+z=30

For all x,y,z ∈ 2n+1 where n∈N(Natural numbers).
Proof:-here’s no combination. It’s impossible. Every number in that list is odd.

We know that any even number can be expressed as 2n where n is an integer. Any odd number can be expressed as 2n−1.

Let m, n, and k all be integers. Then the sum of three odd numbers can be written as:
(2m−1)+(2n−1)+(2k−1)
=2(m+n+k−1)−1.
Note that m+n+k−1 is another integer. If we call it N then the result is simply
2N−1
which, as we know is an odd number. Therefore the sum of three odd numbers is always an odd number.

Hence Proved.

In simple words, there do not have any odd numbers, where by adding any 3 of them we get 30 because

odd + odd + odd
= (odd + odd) + odd
= even + odd
= odd (and 30 is even number)
Example:-

Let the number is 15,13 and 3 then
15=2*7+1
13=2*6+1
3=2*1+1
where 1,6 and 7
now
15+13+3=2*7+1+2*6+1+281+11
=2(7+6+1)+3
=2*14+3(24 is our 'm')
and 2*14≠30.
OR
15+13+3≠30.
CONCLUSION:- So by adding 3 odd numbers, we do not get 30. Is there any other way to do so?
Yes… Read below..

2.) How Possible:-

With using any function within an operator
How Possible?:-

Factorial method:-
3!+11+13=30
3!+9+15=30
3!+3!+3!+3!+3!=30
11+1+3!+3!+3!=30
5+7+3!+3!+3!=30
11+7+3!+3!+3!=30
3+5+7+9+3!=30
1+5+7+11+3!=30
1+1+3!+11+13=30
1+3+5+3!+15=30 and many more.
Click here to Learn How to find Factorial of a program (Mirror Link)
Changing Base method :-
[(3) + (3) + (3) + (3) + (3)] 5= [(6)+(6)+(6)+(6)+(6)]10= [30]10

(1)7+(5)7+(5)7+(5)7+(5)7=(30)710 + 10 + 10 = 30 in any odd base (seven, nine, eleven, and so on).
Click here to learn_base_conversion (Mirror Link)

Addition-Subtraction Method:-
a+b+c=a+b+(x-y) where x-y=c
15+(13-11)+(9+7-5+3-1)=30
15+(13-11)+(9+7-3)=30
15+(13-9)+(7+3+1)=30
15+(13-9)+(7+5-1)=30
15+(13-7)+(5+3+1)=30
15+13+(3-1)=30
15+13+(5-3)=30
15+13+(7-5)=30
15+13+(9-7)=30
15+13+(9-5-3+1)=30
15+13+(11-9-7+5+3-1)=30
15+13+(11-9 )=30
15+13+(11-9+7-5-3+1)=30
15+13+(11-7-5+3)=30
15+13+(11-7-3+1)=30
15+13+(11-5-3-1)=30
OTHER METHOD
1) 30 cm=(15 cm+13 cm)+ 1cm +(7 mm+3mm)
2)( 1+3)+(13+7) +6 (inverting 9 using mirror ) = 30
3) 11.3 + 15.7 + 3 = 30 (Using decimal)
4) 30 years = 15 years + 13 years + 1 year + 7 months + 5 months(USING Calendar Mathematics)
5) ((13+11)/3) + 1 + 5 + 7 + 9 = 30 (using numbers 1, 3, 5, 7, 9, 11, 13)
6) 3 weeks + 1 Day + 7 Days + 13 Hours + 11 Hours = 30 days (USING Calendar Mathematics)
7) (9/3)+(15/5)+(13+1/7)+(11)+(11)=30 (Using Division Operator)
=>3+3+2+11+11=30
Commas were used instead of decimal points in the past history by Arabs and even in France. You will be surprised to hear that even today in some parts of the world. Commas are written instead of decimal unit or a dot!Using commas in place of decimal units we can easily come up with a solution equal to 30!For example:
13,7 + 15,3 + 1 = 30 !

How did you guys post all this on 5-10 mins??? the fock
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help 7 years 11 months ago #485482

me and red are very fast typers

haha

- sent from iphone -
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