full transcript
#### From the Ted Talk by Dennis Shasha: Can you solve the stolen rubies riddle?

## Unscramble the Blue Letters

On the other hand, you can be sure that at least two bxoes have a minimum of 8 rubies. Here’s why. We’ll start by assuming the opposite, that two boxes have 7 or fewer. Those could not be the two that differ by 6, because every box must have at least 2 rubies. In that case, the third box would have at most 13 rubies—that’s 7 plus 6. Add up all three of those boxes, and the most that could equal is 27. Since that’s less than 30, this scenario isn’t possible. You now know, by what’s called a proof by cctiadnrioton, that two of the boxes have 8 or more rubies. If you ask for 8 from all three boxes you’ll receive at least 16— and that’s the best you can guarantee, as you can see by tnkiihng again about the 8, 14, 8 scanerio.
## Open Cloze

On the other hand, you can be sure that at least two **_____** have a minimum of 8 rubies. Here’s why. We’ll start by assuming the opposite, that two boxes have 7 or fewer. Those could not be the two that differ by 6, because every box must have at least 2 rubies. In that case, the third box would have at most 13 rubies—that’s 7 plus 6. Add up all three of those boxes, and the most that could equal is 27. Since that’s less than 30, this scenario isn’t possible. You now know, by what’s called a proof by **_____________**, that two of the boxes have 8 or more rubies. If you ask for 8 from all three boxes you’ll receive at least 16— and that’s the best you can guarantee, as you can see by **________** again about the 8, 14, 8 **________**.
## Solution

- boxes
- thinking
- contradiction
- scenario

## Original Text

On the other hand, you can be sure that at least two boxes have a minimum of 8 rubies. Here’s why. We’ll start by assuming the opposite, that two boxes have 7 or fewer. Those could not be the two that differ by 6, because every box must have at least 2 rubies. In that case, the third box would have at most 13 rubies—that’s 7 plus 6. Add up all three of those boxes, and the most that could equal is 27. Since that’s less than 30, this scenario isn’t possible. You now know, by what’s called a proof by contradiction, that two of the boxes have 8 or more rubies. If you ask for 8 from all three boxes you’ll receive at least 16— and that’s the best you can guarantee, as you can see by thinking again about the 8, 14, 8 scenario.
## Frequently Occurring Word Combinations

## Important Words

- add
- assuming
- box
- boxes
- called
- case
- contradiction
- differ
- equal
- guarantee
- hand
- minimum
- proof
- receive
- rubies
- scenario
- start
- thinking