Matthew Shelborn frequently has to travel for his company, which gives him a chance to meet many people from all parts of the USA. In April, Matthew flew to five different US cities on business and he flew a different airline each time. During each trip he chatted with the person next to him, and no two people he talked to were in the same profession.

From the information, can you determine the date Matthew made each flight (each was on a Monday exactly one week apart starting on April 2nd), the airline he flew, his destination, and the profession of the person who sat next to him on each flight?

1. Three consecutive flights were, in order from first to last, the flight Matthew took with WTA Airways, the flight where he sat next to the teacher, and the flight he took to Atlanta.

2. Matthew sat beside the sports coach on a flight some time earlier in the month than the one he took to Seattle.

3. The week he flew Air Express was some time earlier in the month than the trip to Boston, which was some time earlier in the month than the trip where he sat next to the ballet dancer.

4. It wasn't on the trip to San Diego where Matthew sat next to the doctor.

5. Matthew didn't fly Skyways on his trip to Seattle, and he didn't fly WTA Airways on the trip where he sat next to the sports coach.

6. Atlanta was not Matthew's destination on the trip where he made the acquaintance of the ballet dancer.

7. The Fly America flight was exactly two weeks before the flight where Matthew passed the time chatting with the attorney.

Dates: April 2nd, April 9th, April 16th, April 23rd, April 30th
Airline: Air Express, Fly America, MidUSA Air, Skyways, WTA Airways
Destination: Atlanta, Boston, Chicago, San Diego, Seattle
Seat Mate: Attorney, Ballet Dancer, Doctor, Sports Coach, Teacher

Ans:

Date Airline Destination Seat Mate
April 2nd WTA Airways Chicago Doctor
April 9th Fly America San Diego Teacher
April 16th Air Express Atlanta Sports Coach
April 23rd Skyways Boston Attorney
April 30th MidUSA Air Seattle Ballet Dancer
The trip to Atlanta (1), the trip where Matthew sat next to the ballet dancer (3), and the trip where Matthew sat next to the attorney (7) were among the last three trips [April 16th, 23rd, and 30th (intro)], and the trip to Atlanta wasn't the one where he met the ballet dancer (6) or the attorney [he flew WTA Airways exactly two weeks before the one to Atlanta, and he flew Fly America exactly two weeks before he sat by the attorney (7), thus, these three are separate flights, in some order. He didn't sit by the teacher on the trip to Atlanta (1), so the flight were he sat by the teacher was on one of the first two flights [April 2nd and April 9th (intro)], but it wasn't first [after WTA Airways](1), therefore, April 2nd flight was the WTA Airways flight, the one where he sat by the teacher was the April 9th flight, and the one to Atlanta was the April 16th flight, and he sat by the ballet dancer and attorney on the April 23rd and

April 30th flight, in some order. He didn't sit beside the sports coach on the WTA Airways flight (5) so that wasn't April 2nd, he sat beside the sports coach on the Atlanta flight [April 16th] and it was the April 2nd flight where he sat next to the doctor. April 2nd [first flight, WTA Airways, doctor] wasn't to Seattle (2), Boston (3), or San Diego (4), that flight was to Chicago. The April 9th flight wasn't to Seattle [after sports coach which was April 16th] or to Boston [after Air Express, which would have to be April 2nd, but WTA Airways was April 2nd (1)](3), thus, on April 9th he flew to San Diego. Boston wasn't the last destination (3), so it was his destination on April 23rd and Seattle was his destination on April 30th. Boston [April 23rd] was before the one where he sat by the ballet dancer (3), so he sat by the ballet dancer on April 30th flight to Seattle, and it was on the April 23rd flight to Boston that he sat by the attorney. Since he sat by the attorney on the April 23rd flight, then he flew Fly America on the 9th [exactly two weeks before](7). He flew Air Express before the flight when he flew to Boston [April 23rd](3) so he flew Air Express on the 16th. He didn't fly Skyways to Seattle [April 30th](5), thus, he flew Skyways to Boston on the 23rd and his last flight that month was on MidUSA Air (intro).

How many positive factors of 36,000,000 are not perfect squares?

Question: How many of the positive factors of the number 36,000,000 are not perfect squares.

Any answer without an explanation is spam.





Ans.

My answer is 149.Is it right or wrong??

Here goes my explanation:

36000000=6 x 6 x 10 x 10 x 10 x 10 x 10 x 10
=2 x 3 x 2 x 3 x 2 x 5 x 2 x 5 x 2 x 5 x 2 x 5 x 2 x 5 x 2 x 5
=2⁸ x 3² x 5⁶
Factors possible are:
1
2, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷, 2⁸
3, 3²
5, 5², 5³, 5⁴, 5⁵, 5⁶
For each (2 to 2⁸ and 3 to 3² ) there will be total 16 (8 x 2) combinations of factors having subfactors 2 and 3 only.

2 x 3, 2² x 3, 2³ x 3, 2⁴ x 3, 2⁵ x 3, 2⁶ x 3, 2⁷ x 3, 2⁸ x 3

2 x 3², 2² x 3², 2³ x 3², 2⁴ x 3², 2⁵ x 3², 2⁶ x 3², 2⁷ x 3², 2⁸ x 3²


Similarly for each (2 to 2⁸ and 5 to 5⁶ ) there will be total 48(8 x 6) combinations of factors having subfactors 2 and 5 only.

2 x 5, 2² x 5, 2³ x5, 2⁴ x 5, 2⁵ x 5, 2⁶ x 5, 2⁷ x 5, 2⁸ x 5

2 x 5², 2² x 5², 2³ x 5², 2⁴ x 5², 2⁵ x 5², 2⁶ x 5², 2⁷ x 5², 2⁸ x 5²

2 x 5³, 2² x 5³, 2³ x 5³, 2⁴ x 5³, 2⁵ x 5³, 2⁶ x 5³, 2⁷ x 5³, 2⁸ x 5³

2 x 5⁴, 2² x 5⁴, 2³ x 5⁴, 2⁴ x 5⁴, 2⁵ x 5⁴, 2⁶ x 5⁴, 2⁷ x 5⁴, 2⁸ x 5⁴

2 x 5⁵, 2² x 5⁵, 2³ x 5⁵, 2⁴ x 5⁵, 2⁵ x 5⁵, 2⁶ x 5⁵, 2⁷ x 5⁵, 2⁸ x 5⁵

2 x 5⁶, 2² x 5⁶, 2³ x 5⁶, 2⁴ x 5⁶, 2⁵ x 5⁶, 2⁶ x 5⁶, 2⁷ x 5⁶, 2⁸ x 5⁶

For each (3 to 3² and 5 to 5⁶ ) there will be total 12 (6 x 2) combinations of factors having subfactors 3 and 5 only.

3 x 5, 3² x 5
3 x 5², 3² x 5²
3 x 5³, 3² x 5³
3 x 5⁴, 3² x 5⁴
3 x 5⁵, 3² x 5⁵
3 x 5⁶, 3² x 5⁶

Again for each (2 to 2⁸ and 3 to 3² and 5 to 5⁶ ) there will be total 96 (8 x 2 x 6) combinations of factors having subfactors 2,3 and 5 only.

2 x 3 x 5, 2²x 3 x 5, 2³x 3 x 5, 2⁴ x 3 x 5, 2⁵ x 3 x 5, 2⁶ x 3 x 5, 2⁷ x 3 x 5, 2⁸ x 3 x 5

2 x 3² x 5 , 2²x 3² x 5,2³x 3² x 5, 2⁴ x 3² x 5, 2⁵ x 3² x 5, 2⁶ x 3² x 5, 2⁷ x 3² x 5, 2⁸ x 3² x 5


2 x 3x 5², 2²x 3 x 5², 2³x 3 x 5², 2⁴ x 3 x 5², 2⁵ x 3 x 5², 2⁶ x 3 x 5², 2⁷ x 3 x 5², 2⁸ x 3 x 5²

2 x 3² x 5² , 2²x 3² x 5², 2³x 3² x 5², 2⁴ x 3² x 5², 2⁵ x 3² x 5², 2⁶ x 3² x 5², 2⁷ x 3² x 5², 2⁸ x 3² x 5²


2 x 3x 5³, 2²x 3 x 5³, 2³x 3 x 5³, 2⁴ x 3 x 5³, 2⁵ x 3 x 5³, 2⁶ x 3 x 5³, 2⁷ x 3 x 5³, 2⁸ x 3 x 5³

2 x 3² x 5³ , 2²x 3² x 5³, 2³x 3² x 5³, 2⁴ x 3² x 5³, 2⁵ x 3² x 5³, 2⁶ x 3² x 5³, 2⁷ x 3² x 5³, 2⁸ x 3² x 5³


2 x 3x 5⁴, 2²x 3 x 5⁴, 2³x 3 x 5⁴, 2⁴ x 3 x 5⁴, 2⁵ x 3 x 5⁴, 2⁶ x 3 x 5⁴, 2⁷ x 3 x 5⁴, 2⁸ x 3 x 5⁴

2 x 3² x 5⁴, 2²x 3² x 5⁴, 2³x 3² x 5⁴, 2⁴ x 3² x 5⁴, 2⁵ x 3² x 5⁴, 2⁶ x 3² x 5⁴, 2⁷ x 3² x 5⁴, 2⁸ x 3² x 5⁴


2 x 3x 5⁵, 2²x 3 x 5⁵, 2³x 3 x 5⁵, 2⁴ x 3 x 5⁵, 2⁵ x 3 x 5⁵, 2⁶ x 3 x 5⁵, 2⁷ x 3 x 5⁵, 2⁸ x 3 x 5⁵

2 x 3² x 5⁵ , 2²x 3² x 5⁵, 2³x 3² x 5⁵, 2⁴ x 3² x 5⁵, 2⁵ x 3² x 5⁵, 2⁶ x 3² x 5⁵, 2⁷ x 3² x 5⁵, 2⁸ x 3² x 5⁵


2 x 3x 5⁶, 2²x 3 x 5⁶, 2³x 3 x 5⁶, 2⁴ x 3 x 5⁶, 2⁵ x 3 x 5⁶, 2⁶ x 3 x 5⁶, 2⁷ x 3 x 5⁶, 2⁸ x 3 x 5⁶

2 x 3² x 5⁶, 2²x 3² x 5⁶, 2³x 3² x 5⁶, 2⁴ x 3² x 5⁶, 2⁵ x 3² x 5⁶, 2⁶ x 3² x 5⁶, 2⁷ x 3² x 5⁶, 2⁸ x 3² x 5⁶

And finally 2⁸ x 3² x 5⁶ itself is also a factor
So counting all those factors whose subfactor's exponential power is an even no, I get total no of factors of 36000000 which are not perfect squares as 149.
All such factors are marked in bold.

Find the a,b and c

Find the a,b and c


987654321a + 123456789b + c = (a + b + c)³

Try this kids.

You have to use the mathematical operators in between the numbers to get the correct output....

1 1 1 =6
2 2 2 =6
3 3 3 =6
4 4 4 =6
5 5 5 =6
6 6 6 =6
7 7 7 =6
8 8 8 =6
9 9 9 =6

its very simple ,you all can easily solve it....



Ans:
(1+1+1)! = 6
2+2+2 = 6
3x3-3 = 6
4+4-(sqrt 4) = 6 [positive square root]
(5/5)+5 = 6
6-6+6 = 6
7-(7/7) = 6
8-sqrt(8/(cube root(8))) = 6
(squrt 9) x (sqrt 9) - (sqrt 9) =6