Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #351 2009-02-02 01:06:19

ganesh
Moderator

Online

### 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?

Character is who you are when no one is looking.

## #352 2009-02-02 01:36:25

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #353 2009-02-02 01:42:37

ganesh
Moderator

Online

### Re: Brain Teasers

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

Character is who you are when no one is looking.

## #354 2009-02-02 01:47:54

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #355 2009-02-02 02:41:14

ganesh
Moderator

Online

### 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
?

Character is who you are when no one is looking.

## #356 2009-02-02 03:18:56

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #357 2009-02-02 15:49:11

ganesh
Moderator

Online

### Re: Brain Teasers

Perfectly right, JaneFairfax! Very well done!!!

Character is who you are when no one is looking.

## #358 2009-02-03 02:59:01

ganesh
Moderator

Online

### 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?

Character is who you are when no one is looking.

## #359 2009-02-03 15:39:08

ganesh
Moderator

Online

### 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
?

Character is who you are when no one is looking.

## #360 2009-02-04 01:36:30

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #361 2009-02-04 03:12:45

ganesh
Moderator

Online

### 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?

Character is who you are when no one is looking.

## #362 2009-02-04 09:42:54

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

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

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #363 2009-02-04 15:30:36

ganesh
Moderator

Online

### Re: Brain Teasers

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

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

Character is who you are when no one is looking.

## #364 2009-02-05 01:04:22

ganesh
Moderator

Online

### 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?

Character is who you are when no one is looking.

## #365 2009-02-05 01:16:25

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #366 2009-02-05 01:31:33

ganesh
Moderator

Online

### Re: Brain Teasers

Well done, JaneFairfax!!!

Character is who you are when no one is looking.

## #367 2009-02-05 01:41:30

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #368 2009-02-05 01:46:04

ganesh
Moderator

Online

### Re: Brain Teasers

Both correct, JaneFairfax!

Character is who you are when no one is looking.

## #369 2009-02-05 01:59:45

ganesh
Moderator

Online

### 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

?

Character is who you are when no one is looking.

## #370 2009-02-05 02:31:34

ganesh
Moderator

Online

### Re: Brain Teasers

#268. If

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

Character is who you are when no one is looking.

## #371 2009-02-05 02:57:51

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #372 2009-02-05 16:05:38

ganesh
Moderator

Online

### Re: Brain Teasers

For #268, it would've sufficed if you'd given

.

Character is who you are when no one is looking.

## #373 2009-02-05 21:03:14

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #374 2009-02-06 01:42:33

ganesh
Moderator

Online

### 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?

Character is who you are when no one is looking.

## #375 2009-02-06 08:44:38

JaneFairfax
Legendary Member

Offline

### Re: Brain Teasers

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?