$100, 000 Question Who wants to be a Millionaire
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A: 10-6 < 1, 111, 111 < 10-7
(10-6)-2 < 1, 111, 111-2 < (10-7)-2
10-12 < 1, 111, 111-2. < 10-14 Not a solution
C: 10-10 < 11, 111, 111, 111 < 10-11
Square all as before
10-20 < 11, 111, 111, 111-2 < 10-22 Not a solution
D: 10-11 < 111, 111, 111, 111 < 10-12
Square all as before
10-22 < 111, 111, 111, 111-2 < 10-24 Not a solution
B: 10-8 < 111, 111, 111 < 10-9
Square all as before
10-16 < 111, 111, 111 < 10-18 Possible solution
Assuming one of the solutions must be right, since B is the only possible solution it must be the solution.
Date: 2023-11-15
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Comments and reviews: 22
Devon
There are 17 digits. We know that 111 is close to 1000. When we multiply 10 x 10 =100, so a three digit result from multiply two two-digit numbers. 100 x 100 = 10, 000, a 5 digits result from multiply two three digits. 1000, 000 x 1000, 000= 1000, 000, 000, 000= 13 digit from 7 digits
the pattern thus is twice -minus one. so in the case of 10 x 10, it is 2x2-1 =3, so the result is a three digit number 100. .so if given 100, it would be 3+1=4/2= 2 so if given 17 digits it is 17 +1= 18 divided by 2= 9, so you looking for a 9 digit answer and only B satisfies that. answer B.
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There are 17 digits. We know that 111 is close to 1000. When we multiply 10 x 10 =100, so a three digit result from multiply two two-digit numbers. 100 x 100 = 10, 000, a 5 digits result from multiply two three digits. 1000, 000 x 1000, 000= 1000, 000, 000, 000= 13 digit from 7 digits
the pattern thus is twice -minus one. so in the case of 10 x 10, it is 2x2-1 =3, so the result is a three digit number 100. .so if given 100, it would be 3+1=4/2= 2 so if given 17 digits it is 17 +1= 18 divided by 2= 9, so you looking for a 9 digit answer and only B satisfies that. answer B.
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secret
( Option b ) is answer it-s middle grade maths the logic is: -
The question says same number multiplied by means square root of 12345678987654321 is answer
As we know 11-11=121( means the 11 have 2 digits so you simply count to two then reverse it until you get one means for example
111-111= 12321 because 111 has three digits
Now in the above question the highest digit is 9
Means the answer in the options which have 9 1s a
Is right
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( Option b ) is answer it-s middle grade maths the logic is: -
The question says same number multiplied by means square root of 12345678987654321 is answer
As we know 11-11=121( means the 11 have 2 digits so you simply count to two then reverse it until you get one means for example
111-111= 12321 because 111 has three digits
Now in the above question the highest digit is 9
Means the answer in the options which have 9 1s a
Is right
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Rehyhvkb64
My approach
1x1 is 1
And 11x11 is 121 and 111x111 is 12321
So based and this we can assume that the number of digits will be the middle number in the final answer
For example 11111 has 5 digits, and since there all 1, when it-s multiplied by itself, it will be 123454321.
So the answer will be 111, 111, 111 because it has 9 digits so when it-s squared it will be 12345678987654321
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My approach
1x1 is 1
And 11x11 is 121 and 111x111 is 12321
So based and this we can assume that the number of digits will be the middle number in the final answer
For example 11111 has 5 digits, and since there all 1, when it-s multiplied by itself, it will be 123454321.
So the answer will be 111, 111, 111 because it has 9 digits so when it-s squared it will be 12345678987654321
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Ala
I got the same answer, when I just think that the product has 16 digits after the one. To get this number of digits you need to multiply a number which owns eight digits after one with itself. This can be applied on option be where there are eight digits after 1. This more practical solution if we are considering the limited time that you have in this competition.
suggested answer by Ala' Zayed
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I got the same answer, when I just think that the product has 16 digits after the one. To get this number of digits you need to multiply a number which owns eight digits after one with itself. This can be applied on option be where there are eight digits after 1. This more practical solution if we are considering the limited time that you have in this competition.
suggested answer by Ala' Zayed
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CanadianLoveKnot
I solved instantly by counting the 1000's after the comma of the first whole Number, in this case everything to the right of 12. There are 5 groups of 1000's. When you multiple a number by itself you you double them. Therefore C doesn't work. As. It will give you 6 groups of 1000's and A doesn't work as it will only give you 4. B must be the answer.
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I solved instantly by counting the 1000's after the comma of the first whole Number, in this case everything to the right of 12. There are 5 groups of 1000's. When you multiple a number by itself you you double them. Therefore C doesn't work. As. It will give you 6 groups of 1000's and A doesn't work as it will only give you 4. B must be the answer.
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Kids
How I solved this was - as the answers are in 1, I have considered with 10-10 =100. If you have one zero, it will be doubled if you squared. If you have 1000-1000 =1, 000, 000. So by checking the digits after the first digit I found 16 digits in the questions. That will give us eight zeroes. So it will be just little more than 100, 000, 000. So B has 9 digits.
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How I solved this was - as the answers are in 1, I have considered with 10-10 =100. If you have one zero, it will be doubled if you squared. If you have 1000-1000 =1, 000, 000. So by checking the digits after the first digit I found 16 digits in the questions. That will give us eight zeroes. So it will be just little more than 100, 000, 000. So B has 9 digits.
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Douglas
If you add up the digits in the number in the question you get 81. Sqrt(81) = 9 so you want a number with 9 ones in it. This works because all the possible number to square contain only 0's and 1's (in fact they only contain 1's but if there were some 0's in there too it would still narrow things down but not necessarily give a unique answer.
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If you add up the digits in the number in the question you get 81. Sqrt(81) = 9 so you want a number with 9 ones in it. This works because all the possible number to square contain only 0's and 1's (in fact they only contain 1's but if there were some 0's in there too it would still narrow things down but not necessarily give a unique answer.
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SgtSupaman
This was easier than I thought it would be. I almost instantly intuitively recognized that the 9 turning point would be indicative without even thinking about lower numbers making that evident. From there you can just see 987, 654, 321 has the same number of digits as 111, 111, 111. So, that's the answer.
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This was easier than I thought it would be. I almost instantly intuitively recognized that the 9 turning point would be indicative without even thinking about lower numbers making that evident. From there you can just see 987, 654, 321 has the same number of digits as 111, 111, 111. So, that's the answer.
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Debartha
The answer has 17 digits. Option B has 9 digits. If we think of how we manually multiply, after every row we shift 1 digit to the left. So in second row we shift 1 digit, 3rd row shift 2 digits, and in 9th row shift 8 digits. So we get solution as 17 digit
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The answer has 17 digits. Option B has 9 digits. If we think of how we manually multiply, after every row we shift 1 digit to the left. So in second row we shift 1 digit, 3rd row shift 2 digits, and in 9th row shift 8 digits. So we get solution as 17 digit
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H-seyin
The number obtained as a result of the operation 111111111 x 111111111 is exactly 12345678987654321. this number is the only number that contains all consecutive integer increasing and consecutive integer decreasing digits. #math #mathematics
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The number obtained as a result of the operation 111111111 x 111111111 is exactly 12345678987654321. this number is the only number that contains all consecutive integer increasing and consecutive integer decreasing digits. #math #mathematics
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cbreezy623
10-16 < 12345678987654321 < 10-18 this implies 10-8 < sqrt(12345678987654321) < 10-9. The only option that is between 10-8 and 10-9 is 111111111. This approach is more sound, as he makes an assumption without proving it.
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10-16 < 12345678987654321 < 10-18 this implies 10-8 < sqrt(12345678987654321) < 10-9. The only option that is between 10-8 and 10-9 is 111111111. This approach is more sound, as he makes an assumption without proving it.
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Pragun
My approach
11x11= 121 which is one digit less than total number of digits in multiplication. So by that logic the given number had 17 digits so the multiplying number must have (17+1)/2 digits = 9
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My approach
11x11= 121 which is one digit less than total number of digits in multiplication. So by that logic the given number had 17 digits so the multiplying number must have (17+1)/2 digits = 9
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education
Am I the only one who got it in like 15 seconds? Those are 17 numbers and divided by 2 it is 8, 5 and since where talking about multiplying by itself only the one with 9 numbers would make sense.
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Am I the only one who got it in like 15 seconds? Those are 17 numbers and divided by 2 it is 8, 5 and since where talking about multiplying by itself only the one with 9 numbers would make sense.
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Vineprex
I just rounded 12, 345, 678, 987, 654, 321 to 10, 000, 000, 000, 000, 000 and the squareroot of this number is 100, 000, 000. B is by far the closet to this so I took B
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I just rounded 12, 345, 678, 987, 654, 321 to 10, 000, 000, 000, 000, 000 and the squareroot of this number is 100, 000, 000. B is by far the closet to this so I took B
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Juan
It always amuses me how people emphasises how little it took them to get the correct answer, as if trying to prove to the random person something about themselves.
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It always amuses me how people emphasises how little it took them to get the correct answer, as if trying to prove to the random person something about themselves.
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Fazil
-logically yours
i have done it with digit sum question has a digit sum zero and option 2 when multiply with itself gives digit sum zero too.
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-logically yours
i have done it with digit sum question has a digit sum zero and option 2 when multiply with itself gives digit sum zero too.
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Kevin
the way I did it was the number of digits of answer +(number of digits of answer -1) needs to equal 17 so the only one that did that was B
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the way I did it was the number of digits of answer +(number of digits of answer -1) needs to equal 17 so the only one that did that was B
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Tristan
Easier way would recognising that it-s 1. 23-e16, to get an sqrt(xe16) - ye8, therefore which ever has 9 digits is correct
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Easier way would recognising that it-s 1. 23-e16, to get an sqrt(xe16) - ye8, therefore which ever has 9 digits is correct
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Brian
The number in the question is roughly 10-16 and we want its square root. The answer is the choice that is roughly 10-8. B.
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The number in the question is roughly 10-16 and we want its square root. The answer is the choice that is roughly 10-8. B.
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Prerit
Solved it.
I think ques. doesn't worth this huge amount!
Its easy by taking lower no. as you explained.
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Solved it.
I think ques. doesn't worth this huge amount!
Its easy by taking lower no. as you explained.
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Jayanth
Bad luck. if I was in d hot seat. definitely I would have earn that 100000$. bcozz I answered it correctly.
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Bad luck. if I was in d hot seat. definitely I would have earn that 100000$. bcozz I answered it correctly.
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Don
Product has digits like adding number digits of inputs, exp of sum of log, so B has closest number of digits.
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Product has digits like adding number digits of inputs, exp of sum of log, so B has closest number of digits.
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