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## #351 2009-02-01 02:06:19

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Thanks for the information, JaneFairfax! I wasn't aware of it.

#256. What is the remainder obtained when

is divided by 19?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #352 2009-02-01 02:36:25

JaneFairfax
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## #353 2009-02-01 02:42:37

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Answers to #255, and #256:-

Answer to #256 is perfectly right!
Very well done!!!

Answer to #255:- You made a minor mistake in the calculation. Please try again!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #354 2009-02-01 02:47:54

JaneFairfax
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Registered: 2007-02-23
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## #355 2009-02-01 03:41:14

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Correct, JaneFairfax! Very good!!!

#257. For a positive integer n, let

denote the product of the digits of n, and
denote the sum of the digits of n. What is the number of integers between 10 and 1000 for which
?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #356 2009-02-01 04:18:56

JaneFairfax
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## #357 2009-02-01 16:49:11

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Perfectly right, JaneFairfax! Very well done!!!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #358 2009-02-02 03:59:01

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#258. Four points A, B, C, and D lie on a straight line, such that AB = BC = CD, and the length of AB is 1 meter. An ant at A intends reaching a sugar particle at D. But there are insect repellants kept at points B and C. The ant would not go within 1 meter of the insect repellants. What is the minimum distance in meters that the ant must traverse in order to reach the sugar particle?

#259. In the XOY plane, what is the area of the reegion bounded by the graph of |x+y| + |x-y| = 4?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #359 2009-02-02 16:39:08

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#260. Let n! = 1 x 2 x 3 x 4 x ....n for n≥1. If

,
then what is the remainder when p+2 is divided by
?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #360 2009-02-03 02:36:30

JaneFairfax
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## #361 2009-02-03 04:12:45

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Answers to #258, #259, and #260:
#258 and #260 are correct!
Excellent!

#261. The digits of a three-digit number A are written in the reverse order to form another three digit number B. If B>A, and B-A is perfectly divisible by 7, then which of the following is necessarily true?
(1) 100<A<299
(2) 106<A<305
(3) 112<A<311
(4) 118<A<317

#262. A new flag is to be designed with six vertical stripes using some or all of the colors yellow, blue, gree, and red. What is the number of ways this can be done such that no two adjacent stripes are of the same color?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #362 2009-02-03 10:42:54

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

### Re: Brain Teasers

I think I may have visualized the wrong figure for #259.

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## #363 2009-02-03 16:30:36

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#263. What are the values between which p can lie if

and f(0) and f(1) are of opposite signs?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #364 2009-02-04 02:04:22

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#264. Let

where x is a real number. Then, what is the number of solution(s) the equation
has?

#265. In the figure below, the lines represent one-way roads allowing travel only Northwards or Westwards. Along how many distinct routes can a person from point A reach point B?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #365 2009-02-04 02:16:25

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

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## #366 2009-02-04 02:31:33

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Well done, JaneFairfax!!!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #367 2009-02-04 02:41:30

JaneFairfax
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Posts: 6,868

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## #368 2009-02-04 02:46:04

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Answers to #264 and #265:-
Both correct, JaneFairfax!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #369 2009-02-04 02:59:45

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#266. Let S be the set of five digit numbers formed with the digits 1, 2, 3, 4, and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the unit's place of the numbers in S?

#267. What is the value of x if

?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #370 2009-02-04 03:31:34

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#268. If

where n = 1,2,3,4, ...., then what is
equal to?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #371 2009-02-04 03:57:51

JaneFairfax
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Registered: 2007-02-23
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## #372 2009-02-04 17:05:38

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

Answers to #266, and #268:-
Both answers are correct, JaneFairfax!
For #268, it would've sufficed if you'd given

.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #373 2009-02-04 22:03:14

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

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## #374 2009-02-05 02:42:33

ganesh
Registered: 2005-06-28
Posts: 26,112

### Re: Brain Teasers

#269. In a sequence of seven consecutive integers, he average of the first five integers is n. What is the average of all the seven integers?

#270. One Red flag, three White flags, and two Blue flags are arranged in a line such that no two adjacent flags are of the same color and the flags at the two ends of the line are of different colors. In how many different ways can the flags be arranged?

#271. The integers 34041 and 32506 when divided by a three digit number n leave the same remainder. What is n?

#272. Let S be the set of integers x such that

, x is odd and is divisible by 3 but not by 7. How many elemnts does the set S contain?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #375 2009-02-05 09:44:38

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

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