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Can you solve it? Oxford University Admission Questions | Mathematics

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class= Each friend receives private information about where the surprise is. ?

It is commonly known by all that this and no other information is given.

Host : Do any of you know where the surprise is?

… Long and uncomfortable silence….

Host : Do you know now?

.

Sheila, Colin: (simultaneously): Now I know where it is!

Question. Where is the surprise?

Follow-up: a) Did any of them wait for the first silence? b) What effect did this silence have on your knowledge? How did they learn anything from it? c) Did Colin know that Sheila knew that Colin did not initially know where the surprise was? d) Did any of them wait for the second silence?

3. Alice's boxes.

Alice has invited her friends Caroline and Susan to her house, and has placed several boxes on the table in front of them. The women are all perfectly logical.

  • small red box

  • medium red box

  • large black box

  • small blue box

  • big blue box

Alice tells her friends that she has put a gift in one of the boxes, and privately she has told Caroline the color of the box and Susan the size of the box, and they both know it. The following conversation occurs.

Caroline : I don't know which box is in the gift, and I also know that Susan doesn't.

Susan : I knew before you spoke that you didn't know which box contains the gift.

Caroline : Ah, now that you say that, it suddenly occurs to me which box the gift should contain.

Question. What box is in the gift?

Follow-up: After the conversation, does Susan also know which box is in the gift? If so, who came to know first, Caroline or Susan?

All the riddles come from the drawer of questions from the Oxford interview of mathematical philosopher Joel David Hamkins. Hamkins is Professor of Logic and Sir Peter Strawson Chair of Philosophy at University College, Oxford. He says the university likes candidate students to work through logical reasoning, as this gives them an idea of ​​how they approach thinking about a new topic. “We also got to see a bit of his personality, his tenacity, and his ability to discuss something rationally without knowing everything about it, including his ability to accept helpful suggestions from others. Therefore, the interview not only tests whether they can solve the puzzle on their own in isolation, but we can see how the whole process of their attempted solution unfolds as it happens, and that is what is valuable to the admissions assessment. "

But don't be too smart, these questions won't be used next year!

I'll be back with the solutions at 5pm UK. PLEASE NO SPOILERS

To find more information on the work of Professor Joel David Hamkins, here is his personal website.

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I am the author of several puzzle books, the most recent being the Language Lover's Puzzle Book. I also give school lectures on math and riddles (restrictions allow). If your school is interested, enter tap.

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