BrainDen.com - Brain Teasers 204

3

## Posts posted by jasen

1. ### Rubic cube's face into date

Solve this rubic cube's face into date 2. ### multiply 2 palindrome alphametric to be a pandigital number

There are some different definition of pandigital numbers,
to avoid misinterpretation, lets use this definition :

Pandigital numbers (pandigit) are numbers containing the digits 0-9 which each digit appears exactly once:

Example : 3421567890

Solve this

``````Alphametric Palindrome :  ABCBA
Alphametric Palindrome :  CBABC
----- x
Non Alphametric        : pandigit``````

At a class, the students are going to choose a leader.
The class has 3 groups of students.
Each group contains 4 students.
so total students are 12.
After discussion, they determine this rule :

each students have to vote 1 from each group.
so each students have to vote for 3 persons.
example: if the groups are [a,b,c,d] [e,f,g,h] [i,j,k,l]
each student have to choose 1 from [a,b,c,d], 1 from [e,f,g,h], and 1 from [i,j,k,l]

If someone break the rule, his votes is disqualified.

(To simplify the problem, lets write just initials of the students,
since there is no 2 students has same initials)

`````` 1. [c,d,f]     2. [a,g,c]     3. [d,h,l]    4. [b,e,d]
5. [f,j,g]     6. [g,j,i]     7. [j,i,a]    8. [j,a,f]
9. [b,h,k]     10.[l,c,d]     11.[a,h,l]    12.[g,e,b]
``````

there is 1 vote is disqualified.

The Questions :

• Determine each group members
• Determine which vote is disqualified.
4. ### Traveler problem : Choosing right street between varying answers

A Traveler is going to a town, but he must pass a strange village,
From the village there are 3 streets, only 1 street leads him to the town,
He doesn't know which street he must choose,
The villagers are giving the streets name with numbers written in local symbols,
The traveler can not read the symbols.

1st villager : "Take the street with a cube number."
2nd villager : "Take the street with lowest number."
3rd villager : "Take the street with middle number."
4th villager : "Take the street with higest number."
5th villager : "If you divide the right street number (RSN) with 8, the remaining is 7."
6th villager : "If you divide RSN with 24, the remaining is 15."
7th villager : "If you divide RSN with 12, the remaining is 3."
8th villager : "If you divide RSN with 4, the remaining is 3."
9th villager : "If you divide RSN with 6, the remaining is 3."
10th villager : "If you divide RSN with 5, the remaining is 2."
11th villager : "If you divide RSN with 7, the remaining is 6."

After finding so varying answer, he decided to ask the chief of the village,

The chief than giving him this right information :

``````"we are numbering streets with numbers between 10 to 50,
The left street has lowest number,
The right street has higest number,
The front street has bigger number than left street,
3 villagers give you useless answers,
4 villagers give you right answers,
and 4 villagers give you wrong answers"
``````

What are the street numbers ? Which street he must choose ?

Note :

Useless answer means if you know the numbers, the answer is right to all numbers, so it is useless.
right answer means the answer is leading you only 1 street, and it is the right street.

5. ### Arrange the digits from 0 to 9 into a number with inequality constraints

Arrange the digits from 0 to 9 into a 10 digit number (abcdefghij) which follow the rule :

• a < b > c < d > e < f > g < h > i < j
• difference between 2 adjacent digits is more than 4

Bonus puzzle :

Change the 2nd rule with :

• The digits follow the pattern : even,odd,even,odd....
6. ### Help the police to reveal the hidden password.

9 hours ago, TimeSpaceLightForce said:
Hide contents

Right start. Now decode the message.

7. ### Help the police to reveal the hidden password.

To get more evidence, a police is trying to hack a crimanal's computer.
He find a suspicious transaction file, but it is protected by a password.
Than he find a text file "psw.txt" which he thinks contain the needed password.

He says "What a fool to save the password here"

When he open the text file it is blank.

Help the police to reveal the hidden password.

psw.txt

8. ### when was I born ?

Sorry, the question is wrong, it should be :

I was born just 10 minutes different from my twin brother, But I celebrated my birthday 11 days after my twin brother every year, when was I born ?

9. ### Bar puzzle

To avoid the customers' disappointement, the bartender comes up with a solution.
He gives each man a glass of cocktail, and explains :

If each letter represents a digit, we can write it like this :

1 pepsi + 1 cocacola = 1 cocktail  -> 1 *  40497 + 26212681 = 26253178
2 pepsi + 1 cocacola = 1 cocktail  ->  2 * 27264 + 58535813 = 58590341
3 pepsi + 1 cocacola = 1 cocktail  -> 3 * 20239 + 54515481 = 54576198
4 pepsi + 1 cocacola = 1 cocktail  -> 4 * 18153 + 64606420 = 64679032
5 pepsi + 1 cocacola = 1 cocktail  -> 5 * 12149 + 73707350 = 73768095

10. ### when was I born ?

I was born just 10 minutes different from my twin brother, But I celebrated my birthday 10 days after my twin brother every year, when was I born ?

11. ### sequence 24,60,210,504,1716,2730,...,...

1st clue : Prime numbers.

12. ### sequence 24,60,210,504,1716,2730,...,...

Just now, rocdocmac said:

24, 60, 210, 504, 1716, 2730, 4542, 6738 (??)

wrong.

13. ### sequence 24,60,210,504,1716,2730,...,...

Find next 2 numbers

24,60,210,504,1716,2730,...,...

14. ### All primes

Just now, telesphorelalancette said:

They could be 1, 3 and 5 or 7, 9 and 11. Nice one Jasen!

wrong

Spoiler

only 1 answer,  2,5, 7 no more

5 - 1 = 4, not prime

11 - 7 = 4, not prime

15. ### my conjecture

Thanks Plasmid for your attempt to test this conjecture effectively to 1 trillion.

There is a way to check whether a number is pentagonal, square or triangle, by find out the n-th of the number.

n-th Pentagon x = (1+sqrt(1+24* x)) / 6,  (if n is integer so the number is pentagonal)
n-th Square x = sqrt x,                            (if n is integer so the number is square number)
n-th Triangle x = (sqrt(8*x + 1)-1)/2,         (if n is integer so the number is triangle)

Spoiler

17. ### call chain

There was 25 kids in a class, every kids had some best friends.
To simplify the problem, Let's call each kids with their initial name.
here is a list of kids best friends.

a : [l,h]
b : [k,m,i]
c : [f,l,n,j]
d : [g,m,o]
e : [h,n]
f : [c,m,q]
g : [d,n,r,p]
h : [a,k,q,s,o,e]
i : [b,l,r,t]
j : [c,m,s]
k : [u,r,h,b]
l : [u,w,s,i,c,a]
m : [f,b,d,j,t,x,p,v]
n : [y,w,q,g,c,e]
o : [x,r,h,d]
p : [w,m,g]
q : [x,n,h,f]
r : [u,k,g,i,o,y]
s : [v,l,h,j]
t : [w,m,i]
u : [l,r]
v : [k,m,s]
w : [p,l,n,t]
x : [q,m,o]
y : [r,n]

One day all kids was outside the class room except "a".
then his teacher asked "a" to call one of his best friend to enter the room, "a" called "l".
then the teacher asked "l" to call one of his best friend outside to enter the room, and so on.
after all the call chain, there was no more kids outside, and "s" was the last kids called.

determine the call chain !

18. ### Light Bugs

1 More solution 12 Red, 9 green, 9 blue

Spoiler

R,G,B   R,G,B
5,1,1   7,8,8
8,4,8   4,5,1
3,0,4   9,9,5
4,4,4   8,5,5

19. ### Bar puzzle

Clue :  Convert Letters to Numbers.

20. ### Bar puzzle

5 man enter a bar.
1st man order 1 Pepsi + 1 Coca cola
2nd man order 2 Pepsi + 1 Coca cola
3rd man order 3 Pepsi + 1 Coca cola
4th man order 4 Pepsi + 1 Coca cola
5th man order 5 Pepsi + 1 Coca cola
But they ask the bartender to give them same amount of drinks.

as a logician and mathematician the bartender comes with a solution,
he gives each man a glass of cocktail, and they all happy.

Explain why the bartender gives each man a glass of cocktail ?

21. ### 3 x 3 table with constrains (continued)

If we add 2 matrices from the answer of the puzzle, we will get interesting result, all cells have same result (number 10)

Is There any logic explanation of this ?

3 6 4     7 4 6     10 10 10
8 9 2  +  2 1 8  =  10 10 10
1 5 7     9 5 3     10 10 10

22. ### 4x4 Table, Difference more than 2

Ok, sorry, I 'm wrong, I miss 2 constraints to set the rule..

23. ### 3 x 3 table with constrains

21 hours ago, Pickett said:
Reveal hidden contents

So reflections/rotations get a little strange with this because of the fact that you have stated that the middle-left and middle-middle squares can be a difference of 1. This means if you have a solution that works...and then reflect it across the Y-axis, there's a possibility that that reflected solution is not a valid solution anymore. Here's an example of this:

This solution works with the original configuration:

------ cut  ----

Reflection works vertically

24. ### 4x4 Table, Difference more than 2 Thera are 40 Solutions

25. ### 3 x 3 table with constrains There are 2 solutions, if we rule out Reflection

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