Wednesday
Wednesday: Puzzle Lab, Guess My Rule
Raven sits behind the orange box with a marker and a secret rule written in her notebook.
"Feed me inputs," she says. Rocket slides in a 2. Out comes a 7. He slides in a 5. Out comes a 13.
"Plus 5?" Rocket guesses. "No, 5 plus 5 is 10, not 13." He tries 8. Out comes 19.
"What do you notice about how much the output jumps?" Raven asks.
"From 5 to 8 the input grew 3," Rocket says, "and the output grew 6. Double the jump. So times 2, then something."
Nova hovers over the cards, her light resting on the 2 and the 7. "Two times two is four," she says. "What is left?"
"Three!" Rocket says. "Times 2, plus 3." Raven grins and shows her notebook.
Your mission
Build a rule machine from a box, then play guess my rule. One person hides a rule and the other feeds inputs.
Record every input and output in a table. Use the pattern in the table to find the rule, then write it as an equation.
- A cardboard box with a slot cut in each end (a grown-up cuts the slots).
- Twenty index cards or paper squares and a marker.
- Masking tape to hold the box steady on the bench or table.
- Your Puzzle Notebook and a pencil.
Tape the box down so it does not slide off the bench.
Shoes stay on in the garage. Keep the floor around the bench clear.
- The rule keeper writes a secret rule in the notebook, like × 3 or × 2 + 3, and hides it.
- The guesser writes an input on a card and slides it into the box.
- The rule keeper writes the output on a new card and slides it out the other side.
- Record each pair in a table. After four pairs, the guesser names the rule.
- Check the guess against every row. Then write the rule as an equation and swap roles.
The crew's round
These are the cards from Rocket's turn as the guesser, with Raven keeping the secret rule.
| Input | Output | Ordered pair |
|---|---|---|
| 2 | 7 | (2, 7) |
| 5 | 13 | (5, 13) |
| 8 | 19 | (8, 19) |
| 10 | 23 | (10, 23) |
Reading the pattern: from input 2 to input 5 is a jump of 3. The output jumps from 7 to 13, a jump of 6.
Every step of 1 in the input adds 2 to the output, so the rule starts with × 2. Then 2 × 2 = 4, and 7 is 3 more.
The rule is × 2 + 3, or y = 2x + 3. Check: 2 × 10 + 3 = 23, and the table says 23.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
A rule found from its cards. Tomorrow the crew's folding log shows two rules on one graph.