Jenny overthinks the problem

Jenny spends a lot of her time coming up with strategies for solving the problem, such as asking each number individually whether it’s the goose, or first working out which team is lying.

She is reluctant to start asking any of the ducks any questions until she’s come up with a solution, so spends a long time making notes and drawing matrices in the notebook instead.

Eventually, after thinking very hard about the problem and apparently getting nowhere, she has to go for a walk around the grounds with Tom Cashman to take her mind off of the ducks.

Upon returning from their walk, Tom suggests that maybe Jenny should ask a question. When Jenny asks him how long she’s taken on the task so far, Tom informs her that it’s already been 42 minutes, and that she’s so far not asked a single question.

After reminding herself what the ducks’ responses mean in English, Jenny asks duck number 10 (a truth-telling, red duck) if it is on the team with the goose, and receives one quack in response (yes). Because she has not first identified which team is lying, when Tom asks her what she has learned, she has to acknowledge that she’s not any closer to having an answer.

After more time passes, Jenny eventually asks duck number 1 (a lying, blue duck) “Are you on the team without the goose?”. When she receives two quacks in response (no) she says “yes”, either in acknowledgement of the response, or because she’s correctly worked out that in this case the ‘no’ means ‘yes’.

She then asks duck number 3 (another lying, blue duck) if duck number 10 is the goose and receives one quack in response (yes), before asking duck number 2 (a truth-telling, red duck) if duck number 10 is a duck, and receiving one quack in response (yes). She deduces that if duck number 2 had been lying to her to ‘protect’ duck number 10, then it would say ‘yes’ if number 10 was the goose.

Based on this accurate logic, but having incorrectly identified which team is lying, she then incorrectly accuses duck number 10 of being the goose after 1 hour, 26 minutes, and 49 seconds, and is disqualified from the task.

(Written by Will G and proofread by Karl Craven)

(Illustrations collected and adjusted by: David Fuller)