Supercells And Number Grids

Identify relative magnitudes in a grid and apply constraints to maximize patterns.

5 lessons

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Concept

What is a Supercell?

Define a supercell as a number strictly larger than its top, bottom, left, and right neighbors.

Have you ever noticed patterns in a grid of numbers? In a table, a supercell is a special number that stands out from its immediate neighbors.

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Supercell Condition

Formal rule for supercells.

N > N_{t o p} and N > N_{b o tt o m} and N > N_{l e f t} and N > N_{r i g h t}

A cell

N

is a supercell only if it is strictly larger than all its adjacent neighbors.

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Worked Example

Identifying Supercells

Step-by-step check for supercells in a 1D grid.

Problem. Identify the supercells in the following row of numbers from left to right:

$43, 79, 75, 63, 10, 29, 28, 34$

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reading

Find the Supercells

Identify supercells in a given list of numbers.

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A supercell is a cell containing a number that is strictly greater than all of its immediate neighboring cells. Let's analyze the 1D grid containing the numbers: 6828, 670, 9435, 3780, 3708, 7308, 8000, 5583, and 52. We want to check if the numbers 6828, 9435, and 8000 are supercells by looking at their neighbors.

First, the number 6828 is located at the end of the table and has only one neighbor, which is 670. Since 6828 is greater than 670, is it a supercell? .

Next, look at 9435, which has two adjacent cells: 670 and 3780. Because 9435 is greater than both 670 and 3780, is it a supercell? .

Finally, observe the number 8000, positioned between 7308 and 5583. Since it is larger than both of its adjacent neighbors, is it a supercell? .

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Maximizing Supercells

Determine the maximum number of supercells out of 9 boxes.

If you place 9 different numbers in a row, a cell is a supercell if it is strictly greater than its left and right neighbors.

Your goal is to create as many supercells as possible.

A useful idea: big numbers should sit between smaller numbers, like peaks in a row of hills.

Step 1: What kind of pattern helps create many supercells?*

Think about where the bigger numbers should be placed.

Step 2: Which positions can become supercells?*

Remember: the first and last cells have only one neighbor, so only middle positions can be checked using both neighbors.

Step 3: Why can two supercells not be next to each other?*

A supercell must be greater than both neighbors. Think about what happens if two neighboring cells both try to be supercells.

Step 4: Give one arrangement that creates the maximum*

Try arranging smaller and larger numbers alternately.

Step 5: What is the maximum number of supercells?*

Count the supercells in your arrangement.