full transcript

From the Ted Talk by Alex Rosenthal: Can you solve the rogue submarine riddle?

Unscramble the Blue Letters


Pause now to fgirue it out for yourself. Answer in 3

Answer in 2

Answer in 1

Ignorance-based puzzles like this are notoriously difficult to work through. The trick is to put yourself in the heads of both characters and narrow down the possibilities based on what they know or don’t know.

So let's strat with A's first statement. It means that B could cciovneblay have something with the potential to rvaeel A’s number, but isn’t guaranteed to. That doesn’t sound very definitive, but it can lead us to a major insight. The only scenarios where B could know A’s number are when there’s exactly one valid way to factor B’s number. Try fitaonrcg a few and you’ll find the pattern— It could be prime— where the product must be of 1 and itself— or it could be the product of 1 and the square of a prime, such as 4. In both cases, there is exactly one sum. For a number like 8, factoring it into 2 and 4, or 1, 2, and 4, creates too many onoitps. Because the boss’s numbers must be less than 7, A’s list of B’s possibilities only has these 4 numbers. Here’s where we can conclude a major clue. To think B could have these numbers, A’s nebumr must be a sum of their factors— so 3, 4, 5, or 6. We can eliminate 3 and 4, because if the sum was either, the pcudrot could only be 2 or 3, in which case A would know that B already knows A’s number, contradicting A’s statement.

Open Cloze


Pause now to ______ it out for yourself. Answer in 3

Answer in 2

Answer in 1

Ignorance-based puzzles like this are notoriously difficult to work through. The trick is to put yourself in the heads of both characters and narrow down the possibilities based on what they know or don’t know.

So let's _____ with A's first statement. It means that B could ___________ have something with the potential to ______ A’s number, but isn’t guaranteed to. That doesn’t sound very definitive, but it can lead us to a major insight. The only scenarios where B could know A’s number are when there’s exactly one valid way to factor B’s number. Try _________ a few and you’ll find the pattern— It could be prime— where the product must be of 1 and itself— or it could be the product of 1 and the square of a prime, such as 4. In both cases, there is exactly one sum. For a number like 8, factoring it into 2 and 4, or 1, 2, and 4, creates too many _______. Because the boss’s numbers must be less than 7, A’s list of B’s possibilities only has these 4 numbers. Here’s where we can conclude a major clue. To think B could have these numbers, A’s ______ must be a sum of their factors— so 3, 4, 5, or 6. We can eliminate 3 and 4, because if the sum was either, the _______ could only be 2 or 3, in which case A would know that B already knows A’s number, contradicting A’s statement.

Solution


  1. figure
  2. factoring
  3. options
  4. start
  5. conceivably
  6. reveal
  7. number
  8. product

Original Text


Pause now to figure it out for yourself. Answer in 3

Answer in 2

Answer in 1

Ignorance-based puzzles like this are notoriously difficult to work through. The trick is to put yourself in the heads of both characters and narrow down the possibilities based on what they know or don’t know.

So let's start with A's first statement. It means that B could conceivably have something with the potential to reveal A’s number, but isn’t guaranteed to. That doesn’t sound very definitive, but it can lead us to a major insight. The only scenarios where B could know A’s number are when there’s exactly one valid way to factor B’s number. Try factoring a few and you’ll find the pattern— It could be prime— where the product must be of 1 and itself— or it could be the product of 1 and the square of a prime, such as 4. In both cases, there is exactly one sum. For a number like 8, factoring it into 2 and 4, or 1, 2, and 4, creates too many options. Because the boss’s numbers must be less than 7, A’s list of B’s possibilities only has these 4 numbers. Here’s where we can conclude a major clue. To think B could have these numbers, A’s number must be a sum of their factors— so 3, 4, 5, or 6. We can eliminate 3 and 4, because if the sum was either, the product could only be 2 or 3, in which case A would know that B already knows A’s number, contradicting A’s statement.

Frequently Occurring Word Combinations




Important Words


  1. answer
  2. based
  3. case
  4. cases
  5. characters
  6. clue
  7. conceivably
  8. conclude
  9. contradicting
  10. creates
  11. definitive
  12. difficult
  13. eliminate
  14. factor
  15. factoring
  16. figure
  17. find
  18. guaranteed
  19. heads
  20. insight
  21. lead
  22. list
  23. major
  24. means
  25. narrow
  26. notoriously
  27. number
  28. numbers
  29. options
  30. pause
  31. possibilities
  32. potential
  33. prime
  34. product
  35. put
  36. puzzles
  37. reveal
  38. scenarios
  39. sound
  40. square
  41. start
  42. statement
  43. sum
  44. trick
  45. valid
  46. work