Two Stones Puzzle


Frank owes the merchant Jack a large sum, which Frank is unable to pay. Jack offers Frank a deal: “Convince your daughter Sally to marry me, and I’ll drop the debt.” Frank asks Sally if she’ll marry Jack, but Sally is uninterested. When Jack relates this to Frank, he responds: “I still may be able to help you out. I’ll drop the debt if you convince Sally to agree to the following deal. We all three go to the nearby river. I’ll grab two stones from the river bank, one white and one black. I’ll place the stones in a bag, then hand the bag to Sally. Sally will then pull a single stone from the bag. If Sally draws a black stone, then we’ll be married. If Sally draws white, then we won’t be married. In either case, I’ll drop the debt.” Jack tells Sally the new offer. Sally agrees given the new chances to save her father. However, while at the river Sally sees Jack put two black stones in the bag instead of one black and one white. Sally doesn’t want to ruin the deal by calling Jack out, but she also doesn’t want to marry Jack. What does Sally do?


After I came up with a solution, I looked at others. The standard solution (if there is one), seems to be: Sally draws a stone and quickly drops it into the river before anyone can tell what color it is. Sally then observes the group could determine the color of the stone she dropped by looking at the remaining stone in the bag.

That’s fine; it might work. But I’m not a fan of this solution, as it relies on dropping the stone before anyone can see its color.

I prefer my solution: Sally claims she is superstitious, and that drawing a black stone to start a marriage courts bad luck. Sally proposes that rather than she and the merchant marrying if she draws a black stone, they marry if she draws a white stone. Had the merchant been fair, there would be no reason for him to prefer one color over another, so he should have no grounds for rejecting Sally’s proposal.