there are 9 men and 99 cows?

Question

the 1st cow gives 1 litre of milk
the 2nd cow gives 2 litres of milk
the 3d cow gives 3 litres of milk- - - - - - - - -so on- - - - - - - - - - - - -
the 99th cow gives 99 litres of milk

now divide the cows in such a way that each man gets equal share of milk
(hint-arithematic progressions)

we need to divide the cows to give equal share to 9 men

Answer 1

Well I wish I could think of a more elegant solution, as I'm sure there's a more even distribution of cows (where the first guy doesn't have 6 cows and the last... 30+ cows). Regardless, this solution should work.

First I started by figuring out how much milk each guy was supposed to get. Did this by finding the total amount of milk produced and divided by 9
1+2+...+99 is the sum from 1 to 99

common known arithematic sequence
n(n+1)/2 = sum from 1 to n

Applying this we get
99(100)/2 = 4950 litres

And evenly dividing to the 9men
4950/9 = 550 litres per man

This is where the above posters stopped (at least at the time of this writing)

Next I started by giving one guy as many of the best cows i could without exceeding 550. By best cows I mean the cow that produces the most milks that hasn't already been used.

Once I got the total close to 550, I added the necessary cow to make the total milk 550. For the first 7 cows this only required one additional cow. For the 8th it required 2 (the one cow that would make it 550 was already used). Since it worked for the first 8, It worked for the last since 550 was all that was left over.

Man1
99+ 98+ 97+ 96+95+65 = 550

Man2
94+ 93+ 92+ 91+90+89+1 =550

Man3
88+ 87+ 86+ 85+ 84+ 83+37= 550

Man4
82+81+80+79+ 78+77+73 = 550

Man5
76+75+74+72+71+ 70+ 69+ 43 = 550

Man6
68+67+66+64+63+62+ 61+60+39 = 550

Man7
59+58+57+56+55+54+ 53+52+51+50+5 = 550

Man8
49+48+47+46+45+44+42+ 41+40+38+36+35+ 25+14 = 550

Man9
34+33+32+31+30 +29+28+27+26+24+ 23+22+21+20+19+ 18+17+16+15+13+ 12+11+10+9+8+7+6+4+3+2 = 550

If you want to check these sums It'd probably be easier to just copy paste the sum into google and let google calculator do it

Answer 2

Average yield of the cows = 50 liters each

So, total milk = 99 x 50 = 4950

Number of men = 11

So, amount of milk per each man = 450 liters

So, starting from 1, divide in such a way that the total of each is 450.

Answer 3

Naturally adding them up would give the expression:
1+2+3+...+99
Now add the same expression again but reversed:
99+98+97+...+1
Then you would have 99 of 100's (1+99, 2+98, 3+97...) Therefore the total would be 9900
Divide by 2 because we added each twice, and then divide by 9, each man gets 550L of milk. (That's a lot...*speechless*)

(apology for the missing /2 earlier)

Answer 4

it would be to continually add up 1+2+3+4+5+6... and so on to 99. you would get 4,930 and then you would divide that by the 9 men to get how much they would each get. the answer is 547.77777777 (ongoing so put the line over the first two sevens and.. you know what to do with it)

Answer 5

try adding all the numbers together... so 1+2+3+4+5+6+7+8+9 and so on and then divide to total my the number of men (9) you should get a workable answer.

good luck