FUZZY

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?

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?

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

from when the question starts.

how do you decide the days are equal?

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.

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?

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

how to arrive at the answer?

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?

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?

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

A3 B1 C2 D4 E5 5+2+1+4+3 =15