The Jeweller of Antwerp (A Mathematical Riddle)

Here’s a riddle I came up with, while thinking about the Monty Hall problem and the Unexpected Hanging Paradox.

The Jeweller of Antwerp

Moishe Rosenberg, a wealthy jeweller of Antwerp, called his three sons and two daughters to the parlour. “Children, tonight, we will play a game of chance.” He drew a diamond the size of a small egg from his trouser pocket and held it up so it sparkled in the light.

All eyes were on the diamond as Moishe put it into his left palm, closed his hand around it and hid it behind his back.

He glared at his children over his half-moon glasses. “Listen closely. I have just extended one of my five fingers behind my back. You cannot see it. You must guess.” He paused. “The child who chooses the correct finger will inherit the diamond.” He held up his right hand to hush them. “You must decide who will choose first, who will choose second, and so on.”

First there was silence, and then the children jostled for position. Hershel, the oldest boy, reasoned that it would be best to choose first and pushed to the head of the line. Freda got in second.

Little Rivka was too small and timid to fight for position. She just sucked her thumb and stared at her father with her big eyes.

Moishe Rosenberg looked at his youngest daughter. “You are last, are you?”

She sucked harder on her thumb and nodded.

“Come here,” he said, and called her to look behind him, to see which finger of his left hand he was extending. Then, with his right forefinger he covered his lips. “Shhh. Don’t say anything.”

She smiled and nodded, and stood back in line, guarding her secret carefully.

Moishe Rosenberg turned to Hershel, his oldest son, and held out the five fingers of his right hand. “Choose.”

“It’s not fair,” Hershel said.

“Choose,” Moishe Rosenberg repeated.

“Your thumb,” Hershel guessed.

“Wrong!” Moishe said, and he tucked his thumb in so only four of his fingers were extended. He turned to Freda. “Choose.”

Freda considered her options, then made her choice.

Little Rivka waited her turn, smiling.

Question: Which child had the best chance of inheriting the diamond and why?

Give your best response in the comments.

Leave a comment