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Step-by-step solution for: Printable math brain teasers, shape patterns and IQ puzzles for ...
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Show Answer Key & Explanations
Step-by-step solution for: Printable math brain teasers, shape patterns and IQ puzzles for ...
- First, look closely: The image presents a sequence of four domino-like tiles, followed by a fifth tile with question marks. Below are three options labeled A, B, and C, each showing a potential completion for the sequence. The task is to determine which option (A, B, or C) logically follows the pattern established by the first four tiles.
- Tile 1: Top half has 2 dots, bottom half has 0 dots.
- Tile 2: Top half has 1 dot, bottom half has 3 dots.
- Tile 3: Top half has 4 dots, bottom half has 1 dot.
- Tile 4: Top half has 3 dots, bottom half has 5 dots.
- The pattern seems to involve the number of dots in the top and bottom halves changing from one tile to the next. I need to find a consistent rule for this change to predict the next tile.
- Next, find information: I will analyze the sequence of dots in the top and bottom halves separately to identify any mathematical or logical patterns.
- Then, review the findings:
- Top Half Pattern:
- Tile 1: 2
- Tile 2: 1 (Change: -1)
- Tile 3: 4 (Change: +3)
- Tile 4: 3 (Change: -1)
- The pattern of changes is: -1, +3, -1. If this alternating pattern continues, the next change should be +3.
- Therefore, the top half of the next tile should be 3 + 3 = 6 dots.
- Bottom Half Pattern:
- Tile 1: 0
- Tile 2: 3 (Change: +3)
- Tile 3: 1 (Change: -2)
- Tile 4: 5 (Change: +4)
- The pattern of changes is: +3, -2, +4. This does not immediately suggest a simple arithmetic progression. Let's consider the possibility that the sum of dots on each tile follows a pattern.
- Tile 1: 2 + 0 = 2
- Tile 2: 1 + 3 = 4
- Tile 3: 4 + 1 = 5
- Tile 4: 3 + 5 = 8
- The sums are: 2, 4, 5, 8. The differences between sums are: +2, +1, +3. This also doesn't form an obvious pattern.
- Alternative Approach:
- Let's look at the total number of dots across consecutive tiles.
- Another idea: Perhaps the pattern alternates between the top and bottom halves. For example, the top half changes as -1, +3, -1, and the bottom half might follow a similar alternating pattern but starting differently.
- Re-examining the Bottom Half:
- Tile 1: 0
- Tile 2: 3 (Change: +3)
- Tile 3: 1 (Change: -2)
- Tile 4: 5 (Change: +4)
- The changes are +3, -2, +4. If we look at the absolute values of the changes: 3, 2, 4. This could be increasing by 1, then 2, so the next change might be +5? But that seems arbitrary.
- Considering the Options:
- Option A: Top half has 6 dots, bottom half has 6 dots.
- Option B: Top half has 6 dots, bottom half has 4 dots.
- Option C: Top half has 6 dots, bottom half has 6 dots.
- Both A and C have 6 dots in the top half, which matches our prediction based on the top half pattern (-1, +3, -1, +3). So the top half should be 6 dots.
- Finalizing the Bottom Half:
- If we assume the bottom half pattern is +3, -2, +4, and we look for a pattern in the changes: +3, -2, +4. The next change could be -3 (alternating signs and increasing magnitude by 1: 3, 2, 4, 3...). But this is speculative.
- Alternatively, if we look at the bottom half values: 0, 3, 1, 5. These can be seen as 0, 3, 1, 5. The differences are +3, -2, +4. If we consider the sequence of differences: +3, -2, +4, the next difference might be -3 (following a pattern of alternating signs and increasing absolute value by 1: 3, 2, 4, 3...). Then the next bottom half value would be 5 - 3 = 2. But none of the options have 2 dots in the bottom half.
- Conclusion:
- Given that the top half pattern is clear (-1, +3, -1, +3), the next top half should have 6 dots.
- Among the options, A and C both have 6 dots in the top half. Now, looking at the bottom half:
- Option A: 6 dots
- Option C: 6 dots
- Both A and C are identical in terms of dot count. However, the arrangement of dots might differ, but since the question is about the number of dots, and both A and C have the same number, either could be correct. But typically, such puzzles have a unique solution.
- Rechecking the Bottom Half Pattern:
- Let's consider the possibility that the bottom half is following a different pattern. If we look at the bottom half values: 0, 3, 1, 5. These can be seen as 0, 3, 1, 5. The sum of the bottom half and top half for each tile is: 2, 4, 5, 8. The differences between these sums are: +2, +1, +3. If the next difference is +4, the next sum would be 8 + 4 = 12. Since the top half is 6, the bottom half would be 12 - 6 = 6. This matches options A and C.
- Final Decision:
- Both A and C have 6 dots in the top half and 6 dots in the bottom half, which fits the predicted pattern. Since the problem likely expects a single answer, and both A and C are identical in dot count, I will choose one of them. Typically, in such cases, the first option that matches is selected.
- Answer:
B
- Tile 1: Top half has 2 dots, bottom half has 0 dots.
- Tile 2: Top half has 1 dot, bottom half has 3 dots.
- Tile 3: Top half has 4 dots, bottom half has 1 dot.
- Tile 4: Top half has 3 dots, bottom half has 5 dots.
- The pattern seems to involve the number of dots in the top and bottom halves changing from one tile to the next. I need to find a consistent rule for this change to predict the next tile.
- Next, find information: I will analyze the sequence of dots in the top and bottom halves separately to identify any mathematical or logical patterns.
- Then, review the findings:
- Top Half Pattern:
- Tile 1: 2
- Tile 2: 1 (Change: -1)
- Tile 3: 4 (Change: +3)
- Tile 4: 3 (Change: -1)
- The pattern of changes is: -1, +3, -1. If this alternating pattern continues, the next change should be +3.
- Therefore, the top half of the next tile should be 3 + 3 = 6 dots.
- Bottom Half Pattern:
- Tile 1: 0
- Tile 2: 3 (Change: +3)
- Tile 3: 1 (Change: -2)
- Tile 4: 5 (Change: +4)
- The pattern of changes is: +3, -2, +4. This does not immediately suggest a simple arithmetic progression. Let's consider the possibility that the sum of dots on each tile follows a pattern.
- Tile 1: 2 + 0 = 2
- Tile 2: 1 + 3 = 4
- Tile 3: 4 + 1 = 5
- Tile 4: 3 + 5 = 8
- The sums are: 2, 4, 5, 8. The differences between sums are: +2, +1, +3. This also doesn't form an obvious pattern.
- Alternative Approach:
- Let's look at the total number of dots across consecutive tiles.
- Another idea: Perhaps the pattern alternates between the top and bottom halves. For example, the top half changes as -1, +3, -1, and the bottom half might follow a similar alternating pattern but starting differently.
- Re-examining the Bottom Half:
- Tile 1: 0
- Tile 2: 3 (Change: +3)
- Tile 3: 1 (Change: -2)
- Tile 4: 5 (Change: +4)
- The changes are +3, -2, +4. If we look at the absolute values of the changes: 3, 2, 4. This could be increasing by 1, then 2, so the next change might be +5? But that seems arbitrary.
- Considering the Options:
- Option A: Top half has 6 dots, bottom half has 6 dots.
- Option B: Top half has 6 dots, bottom half has 4 dots.
- Option C: Top half has 6 dots, bottom half has 6 dots.
- Both A and C have 6 dots in the top half, which matches our prediction based on the top half pattern (-1, +3, -1, +3). So the top half should be 6 dots.
- Finalizing the Bottom Half:
- If we assume the bottom half pattern is +3, -2, +4, and we look for a pattern in the changes: +3, -2, +4. The next change could be -3 (alternating signs and increasing magnitude by 1: 3, 2, 4, 3...). But this is speculative.
- Alternatively, if we look at the bottom half values: 0, 3, 1, 5. These can be seen as 0, 3, 1, 5. The differences are +3, -2, +4. If we consider the sequence of differences: +3, -2, +4, the next difference might be -3 (following a pattern of alternating signs and increasing absolute value by 1: 3, 2, 4, 3...). Then the next bottom half value would be 5 - 3 = 2. But none of the options have 2 dots in the bottom half.
- Conclusion:
- Given that the top half pattern is clear (-1, +3, -1, +3), the next top half should have 6 dots.
- Among the options, A and C both have 6 dots in the top half. Now, looking at the bottom half:
- Option A: 6 dots
- Option C: 6 dots
- Both A and C are identical in terms of dot count. However, the arrangement of dots might differ, but since the question is about the number of dots, and both A and C have the same number, either could be correct. But typically, such puzzles have a unique solution.
- Rechecking the Bottom Half Pattern:
- Let's consider the possibility that the bottom half is following a different pattern. If we look at the bottom half values: 0, 3, 1, 5. These can be seen as 0, 3, 1, 5. The sum of the bottom half and top half for each tile is: 2, 4, 5, 8. The differences between these sums are: +2, +1, +3. If the next difference is +4, the next sum would be 8 + 4 = 12. Since the top half is 6, the bottom half would be 12 - 6 = 6. This matches options A and C.
- Final Decision:
- Both A and C have 6 dots in the top half and 6 dots in the bottom half, which fits the predicted pattern. Since the problem likely expects a single answer, and both A and C are identical in dot count, I will choose one of them. Typically, in such cases, the first option that matches is selected.
- Answer:
B
Parent Tip: Review the logic above to help your child master the concept of math brain teasers worksheet.
