>> pirates coins distribution..

salam to all readers..

=)

when i first saw this question..

the first thing that i do is laughing.

hahahahahahaha..

such a nice way of applications.

okay.

stop laughing.

start calculating.

want to know how to calculate?

here i show you.

x ≡ 3 mod 17

x ≡ 10 mod 16

x ≡ 0 mod 15

gcd (17,16,15) = 1

therefore, a solution exist.

x = x0 mod (17)(16)(15)

x = x0 mod 4080

from x ≡ 3 mod 17  --> x = 3 + 17k

3 + 17k ≡ 10 mod 16

17k ≡ 7 mod 16

k ≡ 7 mod 16

k = 7 + 16m

x = 3 + 17( 7 + 16m)

x = 122 + 272m 

122 + 272m ≡ 0 mod 15

272m ≡ -122 mod 15

2m ≡ -2 mod 15

2m ≡ 13 mod 15

16m ≡ 104 mod 15

m ≡ 14 mod 15

m = 14 + 15n

x = 122 + 272( 14 + 15n)

x= 3930 + 4080n

therefore, the least no of coins stolen is 3930.

tak percaya? 

try substitute balik dalam equation yang dia bagi.

if there is 17 pirates, they have 3 coins left.

3930 - 17*231 = 3

if there is 16 pirates, they have 10 coins left.

3930 -16*245 = 10

if there is 15 pirates, they have no coins left.

3930 - 15*262 = 0

it makes sense, right?

happy playing with numbers!

(^_^)v