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Rebuild a Height Order from Its Number Clues

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Number Play · Numbers describing arrangements · 3:08

You'll learn: Use the taller-before counts to rebuild the height order and test claims about it.

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Rebuild a Height Order from Its Number Clues

3:08

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Rebuild a Height Order from Its Number Clues

You'll learn: Use the taller-before counts to rebuild the height order and test claims about it.

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Same topic

Numbers describing arrangements

1

Record How Many Taller People Stand Before Each Person
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Record How Many Taller People Stand Before Each Person
You'll learn: Record, for each person in a line, how many taller people stand before them.

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Parity of sums and differences

3

Predict Whether a Sum or Difference Is Odd or Even
3:01
Predict Whether a Sum or Difference Is Odd or Even
You'll learn: Even ± even and odd ± odd give even; even ± odd gives odd.
Use Odd and Even Counts to Track Bulb Toggles
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Use Odd and Even Counts to Track Bulb Toggles
You'll learn: A bulb toggled an even number of times returns to its start; an odd number flips it.
Predict the Parity of a Sum of Page Numbers
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Predict the Parity of a Sum of Page Numbers
You'll learn: Predict whether a sum of page numbers is odd or even from how many odd numbers it contains.

Next topic

Parity of products

2

Why Does One Even Factor Make a Product Even?
2:57
Why Does One Even Factor Make a Product Even?
You'll learn: Counting grid squares shows that one even factor makes the whole product even.
Why Is a Product of Odd Numbers Always Odd?
3:13
Why Is a Product of Odd Numbers Always Odd?
You'll learn: A product of odd numbers is always odd, because no factor of 2 appears.

Next topic

Parity of expressions

2

Use 2n and 2n + 1 to Explain an Expression's Parity
2:59
Use 2n and 2n + 1 to Explain an Expression's Parity
You'll learn: Write numbers as 2n or 2n + 1 to see when an expression is even or odd for every input.
Can an Incomplete Sequence Support a Parity Claim?
3:15
Can an Incomplete Sequence Support a Parity Claim?
You'll learn: Checking a few cases is not enough; a parity claim needs the complete sequence or a general argument.

Next topic

Number-grid constraints

2

Use Grid Totals and Bounds to Find Missing Numbers
3:05
Use Grid Totals and Bounds to Find Missing Numbers
You'll learn: Use row and column totals and the possible ranges of values to fill a grid's missing numbers.
Check Whether a Number Grid's Clues Can All Be True
3:10
Check Whether a Number Grid's Clues Can All Be True
You'll learn: Check whether all of a grid's clues can be true at once before solving.

Next topic

Constructing magic squares

2

What Do the Magic Sum and Centre Tell Us About a Magic Square?
3:08
What Do the Magic Sum and Centre Tell Us About a Magic Square?
You'll learn: The magic sum and the centre place strong limits on which numbers can go in the corners.
Complete a Magic Square Systematically and Compare Arrangements
3:14
Complete a Magic Square Systematically and Compare Arrangements
You'll learn: One complete magic-square construction needs time for the constraints and completion steps.

Next topic

Generalising magic squares

3

Why Is a 3×3 Magic Square's Sum 3 Times Its Centre?
2:58
Why Is a 3×3 Magic Square's Sum 3 Times Its Centre?
You'll learn: One general magic-square relationship needs a labelled algebraic grid.
Transform a Magic Square by Adding or Scaling Its Entries
3:08
Transform a Magic Square by Adding or Scaling Its Entries
You'll learn: Adding the same number to every entry, or multiplying every entry, keeps a magic square magic.
Build a Magic Square with Sum Zero Using Negative Numbers
3:16
Build a Magic Square with Sum Zero Using Negative Numbers
You'll learn: Use negative numbers to build a magic square whose rows, columns and diagonals all sum to zero.