full transcript

From the Ted Talk by James Tanton: Can you solve the risky disk riddle?

Unscramble the Blue Letters


Let’s consider one possibility. Say that the corrupted disk was this one, and when you come in, no lthigs are on. You could turn 11 on to indicate that disk.

Okay, what if you came in and 11 was already on? You have to switch one light. Which seems like the most innocuous to change? Probably 00, in that if you were to add 00 and 11, you’d still get 11.

So maybe the key is to think of aididton of binary numbers, with the sum of the lit disks communicating the corrupted disk nbmuer.

This works great, until we start with a different hypothetical. What if 00 was the couertrpd disk, and 01 and 10 were on? Here, the sum of the lit disks is 11. But we need to cnhgae this to a sum of 00 with the flip of one switch.

Open Cloze


Let’s consider one possibility. Say that the corrupted disk was this one, and when you come in, no ______ are on. You could turn 11 on to indicate that disk.

Okay, what if you came in and 11 was already on? You have to switch one light. Which seems like the most innocuous to change? Probably 00, in that if you were to add 00 and 11, you’d still get 11.

So maybe the key is to think of ________ of binary numbers, with the sum of the lit disks communicating the corrupted disk ______.

This works great, until we start with a different hypothetical. What if 00 was the _________ disk, and 01 and 10 were on? Here, the sum of the lit disks is 11. But we need to ______ this to a sum of 00 with the flip of one switch.

Solution


  1. change
  2. addition
  3. number
  4. corrupted
  5. lights

Original Text


Let’s consider one possibility. Say that the corrupted disk was this one, and when you come in, no lights are on. You could turn 11 on to indicate that disk.

Okay, what if you came in and 11 was already on? You have to switch one light. Which seems like the most innocuous to change? Probably 00, in that if you were to add 00 and 11, you’d still get 11.

So maybe the key is to think of addition of binary numbers, with the sum of the lit disks communicating the corrupted disk number.

This works great, until we start with a different hypothetical. What if 00 was the corrupted disk, and 01 and 10 were on? Here, the sum of the lit disks is 11. But we need to change this to a sum of 00 with the flip of one switch.

Frequently Occurring Word Combinations


ngrams of length 2

collocation frequency
lit disks 3
corrupted disk 3
binary number 2
disk number 2
turning switch 2


Important Words


  1. add
  2. addition
  3. binary
  4. change
  5. communicating
  6. corrupted
  7. disk
  8. disks
  9. flip
  10. great
  11. hypothetical
  12. innocuous
  13. key
  14. light
  15. lights
  16. lit
  17. number
  18. numbers
  19. possibility
  20. start
  21. sum
  22. switch
  23. turn
  24. works