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# FUZZY

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## Posts posted by FUZZY

1. ### The eldest son

23 hours ago, Thalia said:

@FUZZYI think he means if you list out their ages in order, there will be no repetition and no gaps. So ages 1-19, 2-20, 3-21, etc.

Sum of ages, I would assume applies to eldest sons, not all males.

In araver's solution, S is the sum of ages, X is the oldest son in the village, and Y appears to be the youngest.

I'm not sure where the y-1 came from. If you don't get that either, here's another way of looking at it using the same 3 original equations. Probably just a slightly longer form of his solution.

Thank you Thalia.  Your explanation made both the Q and A very clear.

2. ### The eldest son

On ‎10‎/‎23‎/‎2016 at 4:12 PM, araver said:
Reveal hidden contents

There are 3+4+5+4+3 = 19 huts so 19 ages of the eldest sons in each hut.
Sum of all ages is 5 times the sum of any row which is twice the age of the oldest sun in the village.
There are no gaps and no two are the same so the sum of the 19 ages.
Hence:
(i) S = 10*X
(ii) S = Y + (Y+1) + .... +(Y+18)
(iii) X = Y+18

Rewriting (ii) as a consecutive sum:
S = 19*(Y-1) + (1+....+19) = 19*(Y-1) + 19*20/2
and using (i) and (iii):
10*X = 10*(Y-1)+10*19 = S = 19*(Y-1) + 19*10

Therefore 9*(Y-1) = 0, so Y=1 and X = 19.

Did not use the fact that they are not of voting age (which indeed narrows the possibilities for Y to be either 1 or 2).

when you say the sum of all ages do you mean the sum of the ages of all the eldest sons or sum of the ages of all the male children in the village?

what is Y?

I really like the puzzle.  But I am neither able to completely understand the question or the solution.  Can you throw some light on both?

3. ### The eldest son

On ‎10‎/‎22‎/‎2016 at 5:20 PM, bonanova said:

With a nod to jasen's recent and interesting puzzle,

A traveler happened upon a village of huts, laid out as the circles in the  picture below. The village's mayor explained to the traveler that the family living in each of the huts had an eldest son whose age was unique within the village. (No two eldest sons had the same age.) How interesting, replied the traveler. Tell me this: of all the male children here, what is the age of the very oldest?

The mayor thought for a moment and replied, well I guess I could tell you that none of them are yet of voting age (21), and I guess you might be interested to hear that there are no gaps in their collective ages. But all of that wouldn't be enough information. I think it would be better for you to just knock on all the doors and ask.

I don't have time for that, replied the traveler, and I'm really not that interested. Well, here's an interesting thing about our village, replied the mayor. You may have noticed, our huts are laid out so that many rows of 3, 4, or 5 huts cut across the entire village. Just ask at the huts along any of those rows. Add the ages that you hear, and divide the sum by two. That way you will learn the age of the oldest son in the village.

And now, without knocking on any doors, you can learn it too.

what is meant by " there are no gaps in their collective ages"? Does it mean that the total age of all the male children in every hut is the same number?

4. ### Descendants

On ‎10‎/‎12‎/‎2016 at 3:55 PM, bonanova said:

First thought

Hide contents

2(1000/25) = 240.  About 1.1 trillion>

Edit: Well, that's the number born in the 40th generation.
Adding all the generations gives double that amount.

The first gen (children) are 5 yrs from now as per the question. So, the 25 yrs interval starts from the 2nd gen (grandkids). 1000 yrs from now .....would not it be from 1st gen onwards . Hmm...   how 2^40 ? would not it be < 2^40? Not that it would make a lot of difference, it would still be in trillions, of course! Jus bein' curious .........that's all.

5. ### Probability of finding a three.

On ‎10‎/‎13‎/‎2016 at 2:30 AM, BMAD said:

Suppose there is a hat that contains the numbers 1,2,3,4, and 5.  You seek to find the three. You blindly reach into the hat pulling out a number. If it is wrong, then without replacement you reach for another. When you pull out the three you stop. Each pick before three is subtracted from 0 with your final pick (the three) being added to that total.  What is your expected value?

You could get 3 in the first, second, third, fourth or fifth draws.

3 in the first draw:  One number (3). 1 way

In  the second draw means _ 3 : for the number drawn before 3, it is 4C1 ways.  Then, for 3, it is 1 way. So, 4*1= 4 numbers have 3 in second place. (13,23,43,53)

In the third draw means _ _ 3 : for the two numbers drawn before 3, it is 4C2. The two numbers drawn can arrange themselves in 2! ways. Next, 3 is drawn (1 way).

4C2*2!*1= 12 numbers have 3 in third place.

In the fourth draw means _ _ _ 3 : for the three numbers drawn before 3, it is 4C3. The 3 numbers can arrange themselves in 3! Ways.  Finally, 3 is drawn.

4C3* 3!* 1= 24 numbers have 3 in fourth place.

In the fifth draw means _ _ _ _ 3: for the four numbers drawn before 3, it is 4C4. The 4 numbers can arrange themselves in 4! Ways.  Finally, 3 is drawn.

4C4* 4!*1= 24 numbers have 3 in fifth place.

Totally, 1+4+12+24+24 = 65 numbers have 3 in them.

First draw value = (1/65)*3 = 3/65

Second draw (13 or 23 or 43 or 53) value for the four numbers

=  (1/65)*(0-1+3) + (1/65)*(0-2+3) +  (1/65)*(0-4+3) + (1/65)*(0-5+3)

= 1/65 [–(1+2+4+5)+(3*4)]= 0

Third draw value for the twelve numbers =-36/65

Fourth draw for the 24 numbers = -144/65

Fifth draw = -216/65

Total expected value= (3/65)+0+(-36/65)+(-144/65)+(-216/65)= -393/65

6. ### Descendants

3 hours ago, Buddyboy3000 said:

@FUZZY Does the 1000 years start after your children has two children, or from when the question starts?

from when the question starts.

7. ### Going Picnic or not

23 hours ago, Buddyboy3000 said:
Hide contents

The family was able to go on the picnic.

When it says the certain day was yesterday, and the day before yesterday is yesterday, they are equal to each other. You are only confused by all the words. So, the certain day is the day before yesterday, which is two days ago. Then, the family will go on the picnic the day after tomorrow from the certain day. The family will go on the picnic today. If it rained the day before yesterday, then the family will be able to go on the picnic today.

how do you decide the days are equal?

8. ### Going Picnic or not

Suppose the certain day is Sunday, it would've been yesterday on Monday. The day before yesterday with respect to Monday is Saturday. Saturday would've been yesterday on Sunday.  So, Sunday was yesterday (on Monday) when Saturday was yesterday (on Sunday)?? The first sentence does not make sense.

9. ### Going Picnic or not

A certain day was yesterday when the day before yesterday was yesterday . On that certain day Kim's parents said "we'll go on a picnic the day after tomorrow if it doesn't rain". It rained the day before yesterday but not since.
Did the family go on the picnic?

10. ### Who should do what

 I am not smart enough to understand the procedure explained above.  But I did look up Hungarian algorithm.  I too got 18 as TC. Sorry for the earlier mistake. 1 2 3 4 5 A 8 3 5 4 3 B 2 6 9 4 7 C 6 1 8 4 3 D 5 7 9 8 8 E 5 7 9 4 3 After row minima's subtracted 1 2 3 4 5 A 5 0 2 1 0 B 0 4 5 2 5 C 5 0 7 3 2 D 0 2 4 3 3 E 2 4 6 1 0 After column minima's subtracted 1 2 3 4 5 A 5 0 0 0 0 B 0 4 3 1 5 C 5 0 5 2 2 D 0 2 2 2 3 E 2 4 4 0 0 After assigning zeroes 1 2 3 4 5 A 5 0 0 0 0 B 0 4 3 1 5 C 5 0 5 2 2 D 0 2 2 2 3 E 2 4 4 0 0 Marking unassigned rows 1 2 3 4 5 A 5 0 0 0 0 B 0 4 3 1 5 C 5 0 5 2 2 D 0 2 2 2 3 x E 2 4 4 0 0 Marking columns corresponding to the marked row 1 2 3 4 5 A 5 0 0 0 0 B 0 4 3 1 5 C 5 0 5 2 2 D 0 2 2 2 3 x E 2 4 4 0 0 x Marking row having assigned zero corresponding to the marked column 1 2 3 4 5 A 5 0 0 0 0 B 0 4 3 1 5 x C 5 0 5 2 2 D 0 2 2 2 3 x E 2 4 4 0 0 x Drawing lines through unmarked rows and marked columns 1 2 3 4 5 A 5 0 0 0 0 B 0 4 5 1 5 x C 5 0 5 2 2 D 0 2 2 2 3 x E 2 4 4 0 0 x No of lines not equal to 5.   So, we work further on the table values. After                           subtraction of minimum value among uncovered cells from the latter and adding the min. value at the intersection of the lines 1 2 3 4 5 A 6 0 0 0 0 B 0 3 4 0 4 x C 6 0 5 2 2 D 0 1 1 1 2 x E 3 4 4 0 0 x Assigning zeroes 1 2 3 4 5 A 6 0 0 0 0 B 0 3 4 0 4 C 6 0 5 2 2 D 0 1 1 1 2 E 3 4 4 0 0 A3 B4 C2 D1 E5 TC 5 4 1 5 3 18
11. ### ENLIST + SILENT + LISTEN = ANAGRAM

how to arrive at the answer?

12. ### Descendants

Very few people bother to determine what an amazing potential for overpopulation they have. Let us consider yours. If you and your wife have a meager two children, it would seem you are not adding much to the world. But let's suppose that in 5 years each of your children has two children. In another 25 years, each grandchild has two kids. In another 25 years, each great-grandchild has two offspring-and so on for a thousand years. How many descendants would you have?

13. ### logic or trial&error?

Given the sum and the product of the digits of a 7-digit even number with distinct digits that is divisible by the product, is it possible to figure out the number?

Eg:  Given : sum of the digits=36, product of the digits=18144. Also given:  the 7 digit number with distinct digits is divisible by the product 18144.

how do you figure out the 7-digit even number as 1687392?

14. ### alphametic with modulo

once you know the sum as 36 and the product as 18144, how do you figure out the number as 1687392?

15. ### Who should do what

A3  B1  C2  D4  E5

5+2+1+4+3 =15

16. ### Math puzzle

Samantha=39 ,  Jacob=18

Bonanova got every other number right. kudos!

Ellery=21       Jesse=18     Evelyn=12     Delphine=9

17. ### Math puzzle

 Samantha had three children : Ellery, Jacob and Jesse.Their combined ages totaled half of her age.Five years later, during which time Evelyn was born, Samatha's age equalled the total of  all her children's ages. Ten more years have now passed. Delphine was born during that time.At that event Ellery was as old as Jessy and Evelyn together. The combined ages of all the children are now double Samantha's age, which is only equal to that of Ellery and Jacob together.Ellery's age also equals that of the two daughters.Question : How old are they?     How to arrive at the answer? During the 5 yrs, if Evelyn is born, it could be any number < 5, isn't it? I am clueless as to how to solve this puzzle.

19. ### alphametic puzzle

So you have to assume  c=1 and try 2 to 9 for O? If it is deduced that c=2, then again try all other values for O?

isn't there a shorter and more efficient way of solving?

21. ### Not a friend

one's own reflection.

But,  alive.

22. ### alphametic puzzle

but how is the answer arrived at without using computer?

what is the logic used in arriving at the answers?

23. ### Solve four riddles in one short video (2min 21sec)

Spoiler

mail/greeting card

sausage

can't figure out the matchstick thing

holding hands

the big ben

25. ### Guess me who am I, I am the first on earth, the second in heaven...

the letter 'e'

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