Rocket pins a card to the Puzzle Post board. "Round one: three cards go out to the street. Each card asks the finder to make three more."
"So round two is nine cards," says Raven, "and round three is twenty-seven. What do you notice about the pattern?"
"Tripling," Rocket says. "Three to the something. By round five we run out of index cards."
Nova hovers over the card box, counting with a soft tick. "Three to the fourth is already a lot of cards," she says.
"Then we stop at four rounds," Raven decides, "and add them all up to see how many we made."
Rocket is already writing powers of three down the wall. "This is the best kind of puzzle. The math does the work."
This is the crew's own card count for the Triple Puzzle, made up for the Puzzle Post. Each round hands out three times as many cards as the round before.
| Round | Multiplication | Power | Cards |
|---|---|---|---|
| 1 | 3 | 3¹ | 3 |
| 2 | 3 × 3 | 3² | 9 |
| 3 | 3 × 3 × 3 | 3³ | 27 |
| 4 | 3 × 3 × 3 × 3 | 3⁴ | 81 |
Round 4 alone takes 3⁴ = 81 cards. All four rounds together take 3 + 9 + 27 + 81 = 120 cards.
A power grows fast. Round 4 has 81 cards, but 3 × 4 is only 12. The exponent is a count of factors, never a multiplier.
"Round 3 plus round 2" is the expression 3³ + 3². Powers first: 27 + 9 = 36.
"Twice round 2" is 2 × 3². The power first: 2 × 9 = 18. It is not (2 × 3)² = 36.
| From the card log | True or false? |
|---|---|
| 3³ = 27 | ? |
| Round 4 needs 3 × 4 = 12 cards. | ? |
| 27 + 9 = 36 | ? |
| 3² = 6 | ? |
The card log is read. Tomorrow you find powers in everyday places and review the week.