Math Problem Statement
Solution
Let's go through the problems one by one.
Question 10:
You are asked to create the largest and smallest 3-digit numbers using the digits from the cards: 4, 5, 0, 1, 9.
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Largest Number: To get the largest 3-digit number, we use the three largest digits: 9, 5, and 4. Thus, the largest number is 954.
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Smallest Number: To get the smallest number, we want to use the smallest digits. To avoid a leading zero, we must use the digit 1 as the first digit. Therefore, the smallest number is 104.
Hence, the correct option is:
- C: The largest: 954, the smallest: 104.
Question 11:
The numbers are placed in a grid, and we need to determine the value of A.
Let's analyze the grid:
1 4 9 16 A
2 3 8 15
5 6 7 14
10 11 12 13
The pattern follows a specific logic of filling numbers in an alternating sequence from left to right, then top to bottom.
Looking at the pattern from the first row:
- 1, 4, 9, 16 are all perfect squares (1², 2², 3², 4²), so it seems that A should be the next perfect square, which is 5² = 25.
So, the correct option is:
- D: 25.
Question 12:
The discs of the Othello game alternate between black and white, starting with black. The sequence alternates every two discs.
Looking at the pattern:
- Every third position seems to be a black disc (since black comes after every white disc).
- At the 33rd position, we need to count how many black discs have appeared.
Since the pattern alternates every 2 positions, the number of black discs up to the 33rd position is approximately: Thus, the closest answer is:
- C: 18 discs.
Let me know if you'd like further clarification or details.
Related Questions:
- How can you recognize patterns in number grids like the one in Question 11?
- Why can't zero be the leading digit when forming a 3-digit number?
- What are the mathematical patterns in alternating sequences like those in Othello?
- Can you form other numbers using all five digits in Question 10 and compare their sizes?
- How does the rule of alternating discs in Othello affect different positions in the sequence?
Tip: When working with number patterns, looking for sequences (like squares or primes) often reveals the underlying rule.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Place Value
Formulas
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Theorems
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Suitable Grade Level
Grade 5-7
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