full transcript

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

Unscramble the Blue Letters

You can see for yourself that any starting configuration can sum to any number from 00 to 11 with a flip of a stwich. The reason this works is related to a cnopect called parity. Parity tells you whether a given value is even or odd. In this case, the values whose parity we’re considering are the number of 1s in each digit place of our brnaiy sums. And that’s why we can say that 2 and 0, both even numbers, can be treated as eneqlutiavs. By adndig or subtracting 00, 01, 10, or 11, we can change the parity of either, both, or neither digit, and create the disk number we want.

Open Cloze

You can see for yourself that any starting configuration can sum to any number from 00 to 11 with a flip of a ______. The reason this works is related to a _______ called parity. Parity tells you whether a given value is even or odd. In this case, the values whose parity we’re considering are the number of 1s in each digit place of our ______ sums. And that’s why we can say that 2 and 0, both even numbers, can be treated as ___________. By ______ or subtracting 00, 01, 10, or 11, we can change the parity of either, both, or neither digit, and create the disk number we want.

Solution

  1. adding
  2. equivalents
  3. binary
  4. switch
  5. concept

Original Text

You can see for yourself that any starting configuration can sum to any number from 00 to 11 with a flip of a switch. The reason this works is related to a concept called parity. Parity tells you whether a given value is even or odd. In this case, the values whose parity we’re considering are the number of 1s in each digit place of our binary sums. And that’s why we can say that 2 and 0, both even numbers, can be treated as equivalents. By adding or subtracting 00, 01, 10, or 11, we can change the parity of either, both, or neither digit, and create the disk number we want.

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. adding
  2. binary
  3. called
  4. case
  5. change
  6. concept
  7. configuration
  8. create
  9. digit
  10. disk
  11. equivalents
  12. flip
  13. number
  14. numbers
  15. odd
  16. parity
  17. place
  18. reason
  19. related
  20. starting
  21. subtracting
  22. sum
  23. sums
  24. switch
  25. tells
  26. treated
  27. values
  28. works