**New math problem!**

Assume that each statement is either true or false. What is the

unknown (whole) number from the following possibly

false statements:

-Crook-

unknown (whole) number from the following possibly

false statements:

- At least one of the last two statements in this list is true.
- This is either the first true or the first false statement in the list.
- There exist three consecutive false statements.
- The difference beween the numbers of the last true statement and the first true statement is a factor of the unknown number.
- The sum of the numbers of the true statements is the unknown number.
- This is not the last true statement.
- Each true statement's number is a factor of the unknown number.
- The unknown number equals the percentage of these statements which are true.
- The number of different factors which the unknown number has (excluding 1 and itself) is more than the sum of the numbers of the true statements.
- There are no three cosecutive true statements.

-Crook-

integratdbrains

Branch Unspecified

12 years ago

God forgive me for i cannot answer crooks question!! 😉😀😁😁

By 2, either way 1 must be false, and then so must both 9 and 10.

6, if false, says "This is the last true statement", which gives a paradox, thus

6 must be true, and so must 7 and/or 8.

7 and 8 cannot both be true, as the number had to be a multiple of 6,7,8 , that is a multiple of 168 (by 7), and less than 100 (by 8)

If 8 is false, then 3 is true (8,9,10 is false), if 8 is true, then 3 is false (3 cannot be true when both 6 and 8 are true, then there are no three consecutive statements left).

So we have either

A) F X F X X T F T F F or B) F X T X X T T F F F

In A), 4 and 5 must be true (by false 10), and 2 may be true or false. So by 5 the number shall be either 27 (2+3+4+5+6+7) or 25 (3+4+5+6+7). None of these can fulfill 8, though, so A) is out leaving us with B)

Now, (by 7) 3,6 and 7 are factors, the number must be a multiple of 42, as 2+3+4+5+6+7=27, 5 must be false.

By false 10, 2 and 4 must be true, that is 5 shall be a multiple of the number. Now the number must be a multiple of 2,3,4,5,6 and 7, that is a multiple of 3*4*5*7=420. 420 has 22 different factors

(2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210) and the sum 2+3+4+6+7 = 22, so the only multiple of 420 that fulfills false 9 is 420.

6, if false, says "This is the last true statement", which gives a paradox, thus

6 must be true, and so must 7 and/or 8.

7 and 8 cannot both be true, as the number had to be a multiple of 6,7,8 , that is a multiple of 168 (by 7), and less than 100 (by 8)

If 8 is false, then 3 is true (8,9,10 is false), if 8 is true, then 3 is false (3 cannot be true when both 6 and 8 are true, then there are no three consecutive statements left).

So we have either

A) F X F X X T F T F F or B) F X T X X T T F F F

In A), 4 and 5 must be true (by false 10), and 2 may be true or false. So by 5 the number shall be either 27 (2+3+4+5+6+7) or 25 (3+4+5+6+7). None of these can fulfill 8, though, so A) is out leaving us with B)

Now, (by 7) 3,6 and 7 are factors, the number must be a multiple of 42, as 2+3+4+5+6+7=27, 5 must be false.

By false 10, 2 and 4 must be true, that is 5 shall be a multiple of the number. Now the number must be a multiple of 2,3,4,5,6 and 7, that is a multiple of 3*4*5*7=420. 420 has 22 different factors

(2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210) and the sum 2+3+4+6+7 = 22, so the only multiple of 420 that fulfills false 9 is 420.

xheavenlyx

Electronics and Communication

12 years ago

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come again?

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come again?

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edie4someone

Branch Unspecified

11 years ago

do people in this thread have real lives?

xheavenlyx

Electronics and Communication

11 years ago

So is Jerry correct????Jerryblah... yak yak....blah blah blaah..

..

...blah

...

... ... ...etc

By false 10, 2 and 4 must be true, that is 5 shall be a multiple of the number. Now the number must be a multiple of 2,3,4,5,6 and 7, that is a multiple of 3*4*5*7=420. 420 has 22 different factors

(2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210) and the sum 2+3+4+6+7 = 22, so the only multiple of 420 that fulfills false 9 is 420.

Jeffrey Arulraj

Electronics and Communication

6 years ago

What in the world is the answer

Saandeep Sreerambatla

Branch Unspecified

6 years ago

This is a age old thread! But the question is very good!

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