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Use Odd and Even Counts to Track Bulb Toggles

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Number Play · Parity of sums and differences · 3:03

You'll learn: A bulb toggled an even number of times returns to its start; an odd number flips it.

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Use Odd and Even Counts to Track Bulb Toggles

3:03

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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.

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Same topic

Parity of sums and differences

2

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.
Predict the Parity of a Sum of Page Numbers
3:07
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.

Next topic

Fractions multiplied by whole numbers

1

Multiply a Fraction by a Whole Number Using Repeated Groups
4:01
Multiply a Fraction by a Whole Number Using Repeated Groups
You'll learn: A whole number times a fraction is repeated groups of that fraction.

Next topic

Working with Fractions

1

Multiplying a Fraction by a Whole Number: Repeated Equal Quantities
4:01
Multiplying a Fraction by a Whole Number: Repeated Equal Quantities
You'll learn: Multiplying a Fraction by a Whole Number: Repeated Equal Quantities