I got this problem from math teacher influencer Howie Hua, and gave it to Synapse parents as a Do Now for a Parent Ed presentation. It’s the perfect bite-sized snack that has a relatively low floor, and provides a great challenge.
Spice Level: 🔥🔥🔥⚪⚪
Field of Math: Algebra, Number Theory
Explore the following table of numbers and keep track of any patterns you see. Some guiding questions to point you in the right direction:
Where do you find odd numbers? What do notice as you move left to right? What do you notice as you move top to bottom?
| 1 | 3 | 5 | 7 | … |
| 2 | 6 | 10 | 14 | … |
| 4 | 12 | 20 | 28 | … |
| 8 | 24 | 40 | 56 | … |
| … | … | … | … | … |
Where will you find the following numbers in the table? Give your answer as a row and column. For example, the 24 is in row 4, column 2.
🔥 32
🔥 30
🔥🔥 108
🔥🔥 1000
Once you’ve got the hang of finding numbers, try answering the following spicy questions.
🔥🔥🔥 Will every whole number show up in this table eventually? Prove it.
🔥🔥🔥 Will any number show up more than once in the table? Prove it.
🔥🔥🔥 Describe an algorithm to locate any number in the table.