Lesson 19.2: 3x3 Magic Squares, Grid Logic, and Function Machines
Crack 3x3 magic squares where rows, columns, and diagonals have equal sums, and find input-output function rules.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Mathematical Reasoning and Puzzles
Ancient Chinese scholars discovered the Lo Shu magic square on a turtle shell. Every row, column, and diagonal of 9 distinct numbers summed to exactly 15. Understanding this pattern unlocks spatial reasoning and systematic number placement.
💡 Core Mathematical Concepts: Magic Squares & Function Machines
Focus areas: Magic square, magic constant, input-output machine, function rule.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| Magic Square | A square grid of numbers where every row, column, and diagonal adds up to the same constant sum | Standard 3x3 square uses digits 1 to 9 with sum 15 |
| Magic Constant | The target sum for every row, column, and diagonal | In a 1-9 grid, target sum = 15; center cell is always 5! |
| Input-Output Function Machine | A rule that transforms an incoming number into an outgoing number | Input 4 → Machine → Output 12 (Rule: Multiply by 3) |
| Reverse Operations (Inverse) | Working backwards from the output to find the input by applying the inverse rule | If rule is '+ 7' and output is 20, input was 20 - 7 = 13 |
🔍 Practical Classroom & Everyday Examples
Example 1: Center Cell in a 3x3 Magic Square
In any 3x3 magic square with numbers 1 to 9, the center cell must always be the middle number: 5.
Example 2: Finding the Function Rule
Compare multiple input-output pairs to confirm the rule works for all pairs, not just the first one.
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Checking only rows in a magic square
Correction: You must verify rows, columns, AND both diagonals before declaring a grid a magic square!
Common Error: Assuming function rules only use addition
Correction: Remember rules can be multiplication, division, subtraction, or two-step operations (e.g., × 2 + 1).
🎯 Quick Self-Check Challenge
In an input-output table: Input 3 gives 10, Input 5 gives 16, Input 7 gives 22. What is the rule?
Answer & Explanation:
Rule: Multiply input by 3 and add 1 (3 × 3 + 1 = 10; 5 × 3 + 1 = 16; 7 × 3 + 1 = 22).
🎯 Key Learning Takeaways
Master Mathematical Reasoning and Puzzles fundamentals.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G3-M-CH19-WS05
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 5
Logic Clues, Balance Scales, Magic Squares & Rules (Treasure Island Vault)
G3-M-CH19-WS04
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 4
Logic Clues, Balance Scales, Magic Squares & Rules (Robotics Lab Logic)
G3-M-CH19-WS03
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 3
Logic Clues, Balance Scales, Magic Squares & Rules (Math Olympiad Arena)
G3-M-CH19-WS02
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 2
Logic Clues, Balance Scales, Magic Squares & Rules (Escape Room Quest)
G3-M-CH19-WS01
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 1
Logic Clues, Balance Scales, Magic Squares & Rules (Secret Code Academy)
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
2
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
3
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
4
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
5
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.
6
Short Answer
Medium
1 Mark
Oliver claims that 7, 7, 7 can never form a row in a magic square with sum 21 because magic squares must always have 3 different numbers. Is Oliver correct?
A
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
B
No, magic squares must always use the same number
C
No, 7+7+7 is not 21
D
Yes, because rows cannot add to 21
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
Step-by-Step Explanation:
In a standard mathematical magic square, all entries must be distinct unique numbers.
7
Fill in the Blanks
Medium
1 Mark
Find the missing input: The function rule is 'Subtract 7, then multiply by 2'. The output is 16. What was the input?
A
15
B
14
C
16
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Work backwards: 16 ÷ 2 = 8. 8 + 7 = 15.
8
Fill in the Blanks
Medium
1 Mark
A magic square row contains the numbers [ 8 ], [ ? ], and [ 6 ]. If the magic sum is 24, what number is missing in the middle?
A
10
B
12
C
9
D
14
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10
Step-by-Step Explanation:
8 + 6 = 14. 24 - 14 = 10.
9
Short Answer
Medium
1 Mark
An input-output conveyor machine converts: Input 2 → 8, Input 4 → 16, Input 6 → 24. What will the machine output when the input is 9?
A
36
B
32
C
40
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36
Step-by-Step Explanation:
The rule is 'Multiply by 4'. 9 × 4 = 36.
10
Short Answer
Medium
1 Mark
A lock combination riddle: 'I am a 3-digit number. My hundreds digit is 3. My tens digit is twice my hundreds digit. My ones digit is 1 less than my tens digit.' What is the code?
A
365
B
364
C
354
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
365
Step-by-Step Explanation:
Hundreds = 3. Tens = 3 × 2 = 6. Ones = 6 - 1 = 5. The number is 365.
11
Short Answer
Medium
1 Mark
At the Treasure Island Vault, a balance scale shows that 2 identical brass weights balance a 50g weight and a 30g weight. What is the weight of one brass weight?
A
40g
B
35g
C
50g
D
80g
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
40g
Step-by-Step Explanation:
50g + 30g = 80g. 80g ÷ 2 = 40g each.
12
Multiple Choice
Easy
1 Mark
If 1 Circle + 1 Square = 20 and 1 Circle = 14, what is the value of 1 Square?
A
6
B
7
C
5
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
20 - 14 = 6.
13
Multiple Choice
Easy
1 Mark
If 1 Star + 1 Star + 1 Star = 27, what is the value of 1 Star?
A
9
B
8
C
7
D
6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
27 ÷ 3 = 9.
14
Multiple Choice
Easy
1 Mark
A function machine rule is: 'Multiply input by 4 and add 3'. What is the output for input 5?
A
23
B
20
C
25
D
27
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
23
Step-by-Step Explanation:
(5 × 4) + 3 = 20 + 3 = 23.
15
Multiple Choice
Easy
1 Mark
In a 3x3 magic square using digits 1 to 9, what is the sum of any row, column, or diagonal?
A
15
B
12
C
18
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
The magic sum of a standard 1-9 3x3 square is 15.
16
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
17
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
18
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
19
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
20
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.
21
Short Answer
Medium
1 Mark
Oliver claims that 7, 7, 7 can never form a row in a magic square with sum 21 because magic squares must always have 3 different numbers. Is Oliver correct?
A
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
B
No, magic squares must always use the same number
C
No, 7+7+7 is not 21
D
Yes, because rows cannot add to 21
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
Step-by-Step Explanation:
In a standard mathematical magic square, all entries must be distinct unique numbers.
22
Fill in the Blanks
Medium
1 Mark
Find the missing input: The function rule is 'Subtract 7, then multiply by 2'. The output is 16. What was the input?
A
15
B
14
C
16
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Work backwards: 16 ÷ 2 = 8. 8 + 7 = 15.
23
Fill in the Blanks
Medium
1 Mark
A magic square row contains the numbers [ 8 ], [ ? ], and [ 6 ]. If the magic sum is 18, what number is missing in the middle?
A
4
B
6
C
3
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4
Step-by-Step Explanation:
8 + 6 = 14. 18 - 14 = 4.
24
Short Answer
Medium
1 Mark
An input-output conveyor machine converts: Input 2 → 8, Input 4 → 16, Input 6 → 24. What will the machine output when the input is 9?
A
36
B
32
C
40
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36
Step-by-Step Explanation:
The rule is 'Multiply by 4'. 9 × 4 = 36.
25
Short Answer
Medium
1 Mark
A lock combination riddle: 'I am a 3-digit number. My hundreds digit is 3. My tens digit is twice my hundreds digit. My ones digit is 1 less than my tens digit.' What is the code?
A
365
B
364
C
354
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
365
Step-by-Step Explanation:
Hundreds = 3. Tens = 3 × 2 = 6. Ones = 6 - 1 = 5. The number is 365.
26
Short Answer
Medium
1 Mark
At the Robotics Lab Logic, a balance scale shows that 2 identical brass weights balance a 50g weight and a 30g weight. What is the weight of one brass weight?
A
40g
B
35g
C
50g
D
80g
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
40g
Step-by-Step Explanation:
50g + 30g = 80g. 80g ÷ 2 = 40g each.
27
Multiple Choice
Easy
1 Mark
If 1 Circle + 1 Square = 20 and 1 Circle = 14, what is the value of 1 Square?
A
6
B
7
C
5
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
20 - 14 = 6.
28
Multiple Choice
Easy
1 Mark
If 1 Star + 1 Star + 1 Star = 27, what is the value of 1 Star?
A
9
B
8
C
7
D
6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
27 ÷ 3 = 9.
29
Multiple Choice
Easy
1 Mark
A function machine rule is: 'Multiply input by 4 and add 3'. What is the output for input 5?
A
23
B
20
C
25
D
27
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
23
Step-by-Step Explanation:
(5 × 4) + 3 = 20 + 3 = 23.
30
Multiple Choice
Easy
1 Mark
In a 3x3 magic square using digits 1 to 9, what is the sum of any row, column, or diagonal?
A
15
B
12
C
18
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
The magic sum of a standard 1-9 3x3 square is 15.
31
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
32
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
33
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
34
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
35
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.
36
Short Answer
Medium
1 Mark
Oliver claims that 7, 7, 7 can never form a row in a magic square with sum 21 because magic squares must always have 3 different numbers. Is Oliver correct?
A
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
B
No, magic squares must always use the same number
C
No, 7+7+7 is not 21
D
Yes, because rows cannot add to 21
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
Step-by-Step Explanation:
In a standard mathematical magic square, all entries must be distinct unique numbers.
37
Fill in the Blanks
Medium
1 Mark
Find the missing input: The function rule is 'Subtract 7, then multiply by 2'. The output is 16. What was the input?
A
15
B
14
C
16
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Work backwards: 16 ÷ 2 = 8. 8 + 7 = 15.
38
Fill in the Blanks
Medium
1 Mark
A magic square row contains the numbers [ 8 ], [ ? ], and [ 6 ]. If the magic sum is 30, what number is missing in the middle?
A
16
B
18
C
15
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
16
Step-by-Step Explanation:
8 + 6 = 14. 30 - 14 = 16.
39
Short Answer
Medium
1 Mark
An input-output conveyor machine converts: Input 2 → 8, Input 4 → 16, Input 6 → 24. What will the machine output when the input is 9?
A
36
B
32
C
40
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36
Step-by-Step Explanation:
The rule is 'Multiply by 4'. 9 × 4 = 36.
40
Short Answer
Medium
1 Mark
A lock combination riddle: 'I am a 3-digit number. My hundreds digit is 3. My tens digit is twice my hundreds digit. My ones digit is 1 less than my tens digit.' What is the code?
A
365
B
364
C
354
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
365
Step-by-Step Explanation:
Hundreds = 3. Tens = 3 × 2 = 6. Ones = 6 - 1 = 5. The number is 365.
41
Short Answer
Medium
1 Mark
At the Math Olympiad Arena, a balance scale shows that 2 identical brass weights balance a 50g weight and a 30g weight. What is the weight of one brass weight?
A
40g
B
35g
C
50g
D
80g
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
40g
Step-by-Step Explanation:
50g + 30g = 80g. 80g ÷ 2 = 40g each.
42
Multiple Choice
Easy
1 Mark
If 1 Circle + 1 Square = 20 and 1 Circle = 14, what is the value of 1 Square?
A
6
B
7
C
5
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
20 - 14 = 6.
43
Multiple Choice
Easy
1 Mark
If 1 Star + 1 Star + 1 Star = 27, what is the value of 1 Star?
A
9
B
8
C
7
D
6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
27 ÷ 3 = 9.
44
Multiple Choice
Easy
1 Mark
A function machine rule is: 'Multiply input by 4 and add 3'. What is the output for input 5?
A
23
B
20
C
25
D
27
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
23
Step-by-Step Explanation:
(5 × 4) + 3 = 20 + 3 = 23.
45
Multiple Choice
Easy
1 Mark
In a 3x3 magic square using digits 1 to 9, what is the sum of any row, column, or diagonal?
A
15
B
12
C
18
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
The magic sum of a standard 1-9 3x3 square is 15.
46
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
47
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
48
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
49
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
50
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.