According to my logic when A gives dog from his side to B then A is losing the price of dog so I assumed the equation as 10 - d = c + d d = (10 - c )/2 ------------------(i) Lets start form beginning Suppose price of a cow is x, then total price of cow is x^2. The price per goat is 10 and number of goat is odd. With x^2 sum we have to buy any odd number of goat. For the quotient to be odd while dividing x^2 by 10, remainder always equals 6. Lets check it with these squared numbers. 25 = 2*10 + 5 (even number of goat) 36 = 3*10 + 6 (odd number of goat) 49 = 4*10 + 9 (even) 81 = 8*10 + 1 (enen) 196 = 19*10 + 6 (odd) 256 = 25*10 + 6 (odd) 625 = 62*10 + 5 (even) 676 = 67*10 + 6 (odd) In each case money left after buying even number of goat is 6 which is not other than the money to buy one chicken. Now according to the equation (i) above price of dog becomes 2.