BrainDen.com - New Logic/Math Puzzles

Interleaving strings with overlap

Fri, 20 Nov 2009 20:07:03 +0000

Interleave the three 19-long strings

MOTMMNEEITEAEOENANU
HWOCOMNTSNWOLRYDGSI
TETSOLEHRDHRDTPIDTY

so that they may overlap only at
letters they have in common and
together they form the shortest
possible string (not necessarily
an English sentence).

Here is example solved problem of
this type:
Suppose that the three strings were

HEGOOMOASUTYPOATHII
EISPLLIHTOPRLMTHTSS
RADEXAEFOTONTOEEFBE

Each of these can be stretched out over 45 positions
so that each of the 45 positions is covered by a
letter from at least one of the three. Furthermore,
letters at positions of overlap must agree:

            HE GO O    MOASUTYPO    A T  HII
   EISPLL  IH    TO PRLM    T        HTSS
RADE     XA  EF OTON        T  OEEFB        E

RADEISPLLXAIHEFGOTONPRLMOASUTYPOEEFBAHTSSHIIE

This 45-long string, although not unique, is as
short as possible while fulfilling the requirements
of the problem.

Interleaving strings without overlap

Fri, 20 Nov 2009 20:05:20 +0000

Interleave the three 19-long strings

MOTMMNEEITEAEOENANU
HWOCOMNTSNWOLRYDGSI
TETSOLEHRDHRDTPIDTY

so that they don't overlap and
together they form a 57-long string
which is a good English sentence
with the spaces collapsed out.

Here is example solved problem of
this type:
Suppose that the three strings were

HEGOOMOASUTYPOATHII
EISPLLIHTOPRLMTHTSS
RADEXAEFOTONTOEEFBE

Each of these can be stretched out over 57 positions
so that they do not overlap and each of the 57 positions
is used by at least one of them this way:

HE     GOO    M   O AS  U      T   YP     O      A THI I
   EIS         PL      L  I     H T   O PR  L MTH T   S S
  R   A   DEXA   E F  O  T ONTO  E   E F   B E

HEREISAGOODEXAMPLEOFASOLUTIONTOTHETYPEOFPROBLEMTHATTHISIS

Which is the odd one out?

Fri, 20 Nov 2009 20:02:45 +0000

Which of these words is the odd one out?

easter

homily

jumping

pumpkin

scared

What could you do with this?

Fri, 20 Nov 2009 09:32:49 +0000

HIJKLMNO

weights

Fri, 20 Nov 2009 07:01:18 +0000

there are 5 balls with same shape but different weights; 1,2,3,4,5 grams.
you have an electronic scale. you have to put 3 balls on the scale for every measurement. how many measurement is required at minimum to guarantee to know the weights of all balls.

Circling Numbers

Thu, 19 Nov 2009 18:10:15 +0000

Here's a quick one before the weekend...

You arrange the digits 1 through 9 in a circle (or a modular/wrap around line). You then find the largest sum formed by any three digits in a row from your circle.

What is the smallest sum you can obtain? Show one such solution to the circle.

Consecutive Integers and Sum Puzzle

Thu, 19 Nov 2009 07:16:23 +0000

Prove that the sum of the squares of 2007 consecutive integers cannot be the n-th power of an integer, whenever n is any integer >=2.

Digit Separation and Extreme Values Puzzle

Thu, 19 Nov 2009 07:11:13 +0000

A base ten 10-digit positive integer N contains precisely two 4s, two 3s, two 2s, two 1s and two 0s.

The 4s are separated by four digits, the 3s are separated by three digits, the 2s by two digits, the 1s by one digit and the 0s by no digits.

Determine the respective minimum value and the maximum value of N. It is known that N cannot contain any leading zero.

pleas fallow the rules

Thu, 19 Nov 2009 02:27:13 +0000

There is a land far far away,
That if you opened the door,
You get there almost right away,
The door is hidden in your thoughts,
To dig it up takes quite a lot,
Some take pills,
Others use thrills,
But they never work exactly the same,
Where is this land,
Can you tell me,
And how to get there,
I need to know to.

rules:

don't cheat. no peaking at the spoiler.
read it over and over till you get it.
and no looking at other spoilers.
my oh my this will be fun

Spoiler for

Gibberish????

Wed, 18 Nov 2009 23:14:43 +0000

Personally, I would give this puzzle a difficulty rating of 2 stars, however, it seems more difficult when you don't know how it works.

A mysterious message was found in the school caf�teria, the principal, being the post-9/11 paranoid that he is, fears that this may be a death threat, but his naive vice-principal believes that it simply a bunch of harmless gibberish. The principal is not so easily comforted, so he offers a $50 reward to anyone who can tell him what the message says.

Which day?

Wed, 18 Nov 2009 14:24:19 +0000

Hi,

Need help on this question. On which of the two days of the week, Saturday or Sunday, does New Year's Day fall more often?

How many ways

Wed, 18 Nov 2009 12:23:05 +0000

A robot is given a 4-letter name and 4-letter surname, using the letters of the 26-letter alphabet. None of the letters used in the name is used in the surname.

In how many different ways can this be done?

Example: "VGGA NNEN"

Interesting Poker Puzzle-- If You Like Poker

Wed, 18 Nov 2009 10:15:35 +0000

Here's a poker puzzle. It helps if you have a basic understanding of Hold 'Em.

A dinner host has invited N guests to enjoy a meal. At the end of the meal, he will offer each guest a two card Hold 'Em hand. The winner of the hand will receive a nice door prize. He then deals a rigged three card flop and fourth card in the middle of the table (by rigged, I mean he has set the cards ahead of time). If you know Hold 'Em, you know there is one more card to come. The host does not want anyone to share the door prize, so he must make sure that everyone at the table can still win the entire prize (no ties). But he also wants to make sure that there is at least one card left in the deck that will give each person a winner (the remaining cards are randomly shuffled to ensure a fair outcome).

1. Prove the maximum possible value for N. (remember, everyone is drawing to win the entire prize and there is at least one card left that will give them the win). Hint-- N is greater than the normal 9 or 10 players in a typical Hold 'Em game.

2. Solve for N (there are a few solutions). The solution must include the hands dealt to each person, the four cards in the middle, and the remaining cards left in the deck, and which hand will win with which card/s.

This scenario actually came up at a dinner party I was invited to this summer. Ten of us were "dealt" in and with one more card to come, 9 of us were drawing to a win. We thought the host did a nice job with this little game, but wondered what the max N would be. It turns out there is a max N and there is a solution. Enjoy.

... --- ...!

Tue, 17 Nov 2009 23:12:59 +0000

-.. .- ... �. -.. --- - -.. .- ... �. -.. .- ... �.
-.. .- ... �. -.. .- ... �. -.. .- ... �.
-.. .- ... �.-.. --- - -.. --- - -.. .- ... �. ! crack this one and I'll tell you how good a coconut you've got.

Triplets and Minimum Query Puzzle

Tue, 17 Nov 2009 16:55:38 +0000

There are three identical triplets, Adam, Alan and Alex. It is known that precisely one of them is a truthteller, exactly one of them is a liar and the remaining triad member is an alternator, that is, he alternates true statements and false statements

Frank, who is a mutual acquaintance of the three brothers is currently looking for Adam. He chances upon two of the triplets. Unfortunately, since the brothers look exactly the same he is unable to distinguish between them.

What is the minimum number of questions Frank must ask the duo to guarentee that he can determine which triplet (either one of the two, or the one who's not there) is Adam?

Monthly multiplication and prime puzzle

Tue, 17 Nov 2009 16:39:39 +0000

Solve the following alphametic multiplication puzzle, where each of the capital letters denotes a different base ten digit from 0 to 9. However, each asterisk represents a base ten digit from 0 to 9, whether same or different. None of the numbers can contain any leading zero.

       * * * * * *       
               * *                   
      -------------                  
       * * * * * *                    
     * * * * * *                       
    ---------------                    
     O C T O B R E                
                                          
                                          

where each of OCTO, CTO, CTOB, TO, TOBR, TOBRE, OBRE,  BRE, 
BR,  RE and E is a prime number.

Street racing

Mon, 16 Nov 2009 12:56:24 +0000

I was sitting in my car by the side of a highway, when i saw a car coming from behind.
I started my engine and only when the distance between that car and mine was 10x i started moving.
Though that car was moving with a constant speed 10x/3 and i was accelerating uniformly, after i drove for a distance 10x,
that car became exactly next to me.
At that exact moment i decreased my acceleration to the half, and drove for a distance of 45x/4 and the distance separating us became 12.5M (41.01ft)

Which of the following cars could i possibly be driving?

- SEAT ALTEA TDI 2.0 DSG
- FERRARI F50
- TECHART PORSCHE CAYENNE TURBO
- LOTUS EXIGE
- Mercedes G55 AMG
- Levent-Sisli Suzuki DL650 V-Strom

Notes:
- He's never in the front.
- The movement is linear.

Spoiler for hint

Greatest value of M

Sat, 14 Nov 2009 15:08:39 +0000

I have chosen two different numbers greater than N but less than M. I tell their sum to Mr. S and their product to Ms. P. The following conversation ensues:
Mr. S: I cannot determine the two numbers.
Ms. P: I cannot determine the two numbers either.
Mr. S: I still cannot determine the two numbers.
Ms. P: Now I can determine the two numbers.
Mr. S: Now I can determine the two numbers also.
Find the greatest value of M for which this puzzle has a unique solution, for N=1, N=2 and N=3.

Find value of x, y ,z

Sat, 14 Nov 2009 14:24:18 +0000

If x, y, z all are positive integers... then

31x^3 - y^3 = z^3.

Now, if you consider non-positive integer solutions then..

(0, -1, 1) and (42, -65, 137) are some of the solutions...

So, find out positive solutions only

Please Help

Sat, 14 Nov 2009 05:22:22 +0000

I always have difficulty with logic puzzles. Usually, I miss making inferences that really make the puzzle's solution flow out. Are there any good books/resources that train people on logic puzzles? (I moved this from the brain teaser forum)

The kind of puzzle I'm talking about would go something like this:

Five bidders at an auction are hoping to secure a particularly nice piece of china. From the information given, can you work out where each is standing in the room, his or her bid, and the covert method of signaling each uses to indicate their bid to the auctioneer?

1. The initial bid of $200 was made by nodding, but not by the bidder in the middle of hte room.

2. Mr. Lott raised it to $225, but not by raising his finger; the bid made by that means was lower than Mr. Gowing's.

3. Mrs. Gavell didn't take the price to $250; the person standing on the right raised the bid to $275.

4. Mrs. Nock touched her ear to register her bid, but it was lower than that of the person sitting in the front row.

5. The bidder standing to the left signaled a bid by raising his or her programme slightly.

6. Mr. Sayle was standing in the back of the auction room.

Bidders: Mrs. Gavell, Mr. Gowing, Mr. Lott, Mrs. Nock, Mr. Sayle

Signal Method: Nodding, raising finger, raising programme, Touching ear, winking

Bid: 200, 225, 250, 275, 300

Position: Front row, middle, standing at back, standing left, standing right

All of the problems I'm referring to are of this format. It's not just this particular puzzle giving me trouble, it's all puzzles of this format. I tried using the grid that they give in the book, but that doesn't help. There has to be a way to learn to master these, right? Please help! Thanks.

A Twist on Decimal Code

Fri, 13 Nov 2009 20:10:12 +0000

I thought I'd put my twist on xamdam's decimal code. Just decrypt the following:

5.50 --- 15.75 --- 325.150 --- 69.92 --- 147.84 --- 95.38 --- 68.187 --- 150.45 --- 20.260 --- 54.36 --- 16.112 --- 182.70 --- 224.84

Great families

Fri, 13 Nov 2009 06:35:35 +0000

Three families make a remarkable discovery. The sum of the ages of their members are all the same, the sum of the squares of the ages of their members are all the same, and the sum of the cubes of the ages of their members are all the same. Everyone in all 3 families has a different age, and nobody is more than 100 years old.

What is the smallest possible sum of their ages? Can this be done with 4 families?

Where did all the people go George?

Thu, 12 Nov 2009 01:55:21 +0000

I hope no one has posted anything like this before... so here it goes....

A bus full of people is traveling over a bridge on its way to Las Vagas. No one gets on or off, but, when the bus arrives in Las Vagas there's not a single person on board. How can this be possible??????????

Four individuals and liar identification puzzle

Wed, 11 Nov 2009 17:23:13 +0000

Each of the four persons P, Q, R and S are thinking of the same number. When a passersby asked what number they are thinking of, the four individuals respond as follows:

• P: The number has two digits.
• Q: The number is a divisor of 150.
• R: The number is not 150.
• S: The number is divisible by 25.

However, precisely one of these individuals is a liar, while the remaining three are truthtellers.

Identify the liar from the abovementioned statements.

Factorial vs Exponential

Wed, 11 Nov 2009 10:57:54 +0000

Which has the greater value

101²⁰⁰ or 101*(200!) ?

Duodecimal positive integer, divisibility and 26th digit puzzle

Wed, 11 Nov 2009 08:41:05 +0000

N is a 50-digit duodecimal (base 12) positive integer. All the digits of N is 1 except the 26th digit (reading left to right).

Reading left to right, what is the 26th digit of N, given that the duodecimal number 17 divides N?

A Moving Problem

Tue, 10 Nov 2009 11:29:10 +0000

A ribbon comprises a line of squares numbered sequentially from 0 to n. A marker can initially be placed on any square. After positioning such a marker, it may be repositioned by moving it p squares to the right or q squares to the left, provided that one does not fall off the ribbon. The numbers p and q are mutually co-prime.

Show that n = p + q � 2 is the smallest value for n which permits all squares to be visited after a successive number of moves.

game&strategy

Tue, 10 Nov 2009 07:51:36 +0000

you are playing a game with your friend on a 7x7 chess board.
you begin first and put a "0"(zero) on any square on the board, then your friend puts a "1"(one);
next you put zero, then your firend puts one...
game is going on so until all squares are marked with zero's and one's.
afterthat sum of the numbers in each row and column are notted;

i)odd numbers of those summed numbers go to you,
ii)even numbers of them go to your friend,

you and your friend add your numbers,the one whose collected number is higher than the others wins the game.

Question:

assuming that you and your friend play the game without any mistake/fault(i.e. both are expert on this game),
what can be the maximum number that you can get?

New Genetics Problems

Mon, 09 Nov 2009 22:18:08 +0000

There is an effect that only shows when someone is homozygous recessive for the trait. This phenotype shows in one certain female, who has a child with a male who does NOT show the trait. not all females get this effect, and males can also get it too. The couple has a child that shows the effect [which is being homozygous recessive]. They have another child who also shows the effect. Then they have a THIRD child who shows the effect.

What WAS the probability before it was born that the first child would show the recessive phenotype?
What WAS the probability before IT was born that the second child would show the phenotype?
What WAS the probability before IT was born that the third child would show the phenotype?

This is the answer...

Spoiler for My Answer

Two Urns and Two Colored Balls Puzzle

Mon, 09 Nov 2009 18:51:08 +0000

From urn A containing 4 white and 8 black balls, 6 balls are transferred into an empty urn B. Three balls are now drawn from urn B, and each of them happens to be white.

Determine the probability that a fourth ball drawn from urn B will be white, if:

(I) The first three balls are returned to urn B.

(II) None of the first three balls are returned to urn B.

Powers, Six digit Numbers and Substitution Puzzle

Mon, 09 Nov 2009 18:44:27 +0000

Substitute each of the capital letters by a different base ten digit from 1 to 9, to satisfy this set of cryptarithmetic equations. Each of F, G, H and I represents an odd digit.

GBIGBE = (EDB)^D, and:

ADBADF = (HDH)^D, and:

HGAHGC = (BEC)^D

Spheres in a cone

Sun, 08 Nov 2009 12:41:58 +0000

An infinite amount of spheres are placed in a cone with a half angle x (0
(total volume of spheres) / (volume of cone)

I hope this one last more than 30 minutes this time.

Bad Poll

Sun, 08 Nov 2009 10:24:11 +0000

Today I came across a website that has a daily poll. Today the question was

'How often do you visit this site?'
1. About once a day (75%)
2. About once a week (20%)
3. About once a month (4%)
4. About once a year (1%)

I have simplified the options and results for the purpose of this puzzle. Assume that everyone can fit into one of the four categories. However, it should hopefully be obvious to a statistician (probably no so much to the people who posted the poll) that the results are not representative.

Can you adjust the results of this poll to give more representative data?

square-free

Sun, 08 Nov 2009 03:08:40 +0000

the classic square free sequence (a sequence of digits such that no adjacent sequence of any length is the same) is fairly widely known.

0
12
1020
10212012
...
the next line is generated by 3 substitution rules,
0 -> 12
1 -> 102
2 -> 0
you might note that the length of the sequence always is a power of 2.

now for the puzzle:
can you create substitution rules for 0,1,2,3 such that the sequence is square free and length of the sequence is powers of 3?

Acid and two representations puzzle

Sun, 08 Nov 2009 02:11:17 +0000

Substitute each of the letters by a different base ten digit from 1 to 9 to satisfy the following alphametic equation.

ACID = B^F + E^F + G^F = H^F + I^F + D^F

Eight Digit Number and Summed Power Puzzle

Sun, 08 Nov 2009 01:51:23 +0000

Substitute each of the capital letters by a different base ten digit from 0 to 8 to satisfy each of the following cryptarithmetic relationships.

(I) ABCDEFGF = A^E + B^E+ C^E+ D^E+ E^E+ F^E+ G^E+ F^E
where, each of A and E is nonzero, and:

(II) ABCDEFGF does not contain the digit 1, and:

(III) Reading from left to right, nonzero even digits appear in ascending order of magnitude, but odd digits appear in descending order of magnitude in ABCDEFGF.

Fiftieth Derivative Puzzle

Sun, 08 Nov 2009 01:43:41 +0000

Let f(x) = (x+1)²*e^2x.

The fiftieth derivative f ⁽⁵⁰⁾(0) can be expressed in the form k*2ⁿ where k is an odd integer and n is a positive integer.

Find k and n.

and finally!

Sat, 07 Nov 2009 23:48:02 +0000

Can you write a sentence that is perfectly logical, meaningful and correct that has the word "and" repeated five times in a row?

The Decimal Code

Sat, 07 Nov 2009 21:51:59 +0000

42.63 --- 19.95 --- 10.75 --- 5.5 --- 66.88 --- 35.15 --- 54.72 --- 50.75 --- 46.92 --- 40.8 --- 63.99 --- 90.18 --- 4.72 --- 24.36 --- 31.62 --- 46.46 --- 72.72 --- 25.45 --- 36.54

ENDDROOPACORNTHINKERSMANANDNOTYOUMORENOTSPIDERLOW

How many factors?

Sat, 07 Nov 2009 14:08:08 +0000

X is the product of p prime numbers. None of the factors of X are square (except 1). How many factors does Xⁿ have?