This is similar to another question "How did Judas Die", but is specifically addressing another aspect of the story.
In Matthew we have the priests purchasing the field:
5 And he threw the pieces of silver into the temple sanctuary and departed; and he went away and hanged himself. 6 The chief priests took the pieces of silver and said, “It is not lawful to put them into the temple treasury, since it is the price of blood.” 7 And they conferred together and with the money bought the Potter’s Field as a burial place for strangers.
And in Acts we have Judas purchasing it:
16 “Brethren, the Scripture had to be fulfilled, which the Holy Spirit foretold by the mouth of David concerning Judas, who became a guide to those who arrested Jesus. 17 For he was counted among us and received his share in this ministry.” 18 (Now this man acquired a field with the price of his wickedness, and falling headlong, he burst open in the middle and all his intestines gushed out.
This seems a clear contradiction in the New Testament. What is going on here?