Reasoning: How to Solve Dice Positions - Finding Hidden Numbers on Adjacent Faces

Introduction

"Mastering Dice Positions can fetch you 10-15 marks in competitive exams, making it a must-know topic to crack the exam quickly and confidently."

WHAT YOU NEED TO KNOW FIRST

To solve Dice Positions, you need to have the following basic concepts on your fingertips:

1. Direction Chart: A simple chart showing the adjacent faces of a cube (up, down, left, right, front, back).
2. BODMAS: A mnemonic to remember the order of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
3. Sitting Arrangement Conventions: Understanding how people are seated in a room (e.g., clockwise, anti-clockwise, random).

CRYSTAL‑CLEAR METHOD (Step‑by‑Step)

To find the hidden numbers on adjacent faces, follow these steps:

1. Draw a direction chart: Draw a simple chart showing the adjacent faces of a cube.
2. Identify the given information: Read the given information carefully and identify the numbers on the visible faces.
3. Use BODMAS: Apply BODMAS to evaluate any mathematical expressions given in the problem.
4. Find the hidden numbers: Use the direction chart and given information to find the hidden numbers on adjacent faces.
5. Verify the answer: Check your answer by applying BODMAS and ensuring that the numbers on adjacent faces match.

WORKED EXAMPLES

Example 1 – Easy

Problem: Find the hidden number on the face opposite to the face with number 5.

Solution:

1. Draw a direction chart: Up | Down

Left | Right

Front | Back

1. Identify the given information: The face with number 5 is on the front side.

2. Use BODMAS: No mathematical expression is given.

3. Find the hidden numbers: Since the face with number 5 is on the front side, the hidden number on the face opposite to it will be on the back side. Therefore, the hidden number is 5.

4. Verify the answer: The numbers on adjacent faces match (5 on the front and 5 on the back).

What we learned: To find the hidden number on the face opposite to the face with number 5, we need to use the direction chart and identify the given information.

Example 2 – Medium

Problem: Find the hidden number on the face adjacent to the face with number 3, given that the face with number 2 is on the left side.

Solution:

1. Draw a direction chart: Up | Down

Left | Right

Front | Back

1. Identify the given information: The face with number 2 is on the left side, and the face with number 3 is adjacent to it.

2. Use BODMAS: No mathematical expression is given.

3. Find the hidden numbers: Since the face with number 2 is on the left side, the face with number 3 will be on the right side. The hidden number on the face adjacent to it will be on the front side. Therefore, the hidden number is 3.

4. Verify the answer: The numbers on adjacent faces match (3 on the right and 3 on the front).

What we learned: To find the hidden number on the face adjacent to the face with number 3, we need to use the direction chart and identify the given information.

Example 3 – Exam-Style

Problem: Find the hidden number on the face opposite to the face with number 7, given that the face with number 4 is on the front side and the face with number 9 is on the back side.

Solution:

1. Draw a direction chart: Up | Down

Left | Right

Front | Back

1. Identify the given information: The face with number 4 is on the front side, the face with number 9 is on the back side, and the face with number 7 is opposite to it.

2. Use BODMAS: No mathematical expression is given.

3. Find the hidden numbers: Since the face with number 4 is on the front side, the face with number 9 is on the back side. The face with number 7 will be on the opposite side, which is the up side. Therefore, the hidden number is 7.

4. Verify the answer: The numbers on adjacent faces match (7 on the up side and 7 on the down side).

What we learned: To find the hidden number on the face opposite to the face with number 7, we need to use the direction chart and identify the given information.

Common Mistakes

MISTAKE → WHY IT HAPPENS → CORRECT APPROACH

1. Mistake: Assuming the direction chart is not necessary. WHY IT HAPPENS: Students may think that they can solve the problem without drawing a direction chart. CORRECT APPROACH: Always draw a direction chart to visualize the adjacent faces.

2. Mistake: Not using BODMAS. WHY IT HAPPENS: Students may forget to apply BODMAS to mathematical expressions. CORRECT APPROACH: Always apply BODMAS to evaluate mathematical expressions.

3. Mistake: Not verifying the answer. WHY IT HAPPENS: Students may not check their answer carefully. CORRECT APPROACH: Always verify the answer by checking the numbers on adjacent faces.

4. Mistake: Not identifying the given information correctly. WHY IT HAPPENS: Students may misread the given information. CORRECT APPROACH: Always read the given information carefully and identify the numbers on the visible faces.

5. Mistake: Not using the direction chart correctly. WHY IT HAPPENS: Students may not understand how to use the direction chart. CORRECT APPROACH: Always use the direction chart to find the hidden numbers.

EXAM TRAPS

Trap → How to Spot it → How to Avoid it

1. Trap: The direction chart is not provided. How to Spot it: Check if the direction chart is provided or if you need to draw it. How to Avoid it: Always draw a direction chart to visualize the adjacent faces.

2. Trap: The given information is incomplete. How to Spot it: Check if the given information is complete and clear. How to Avoid it: Always read the given information carefully and identify the numbers on the visible faces.

3. Trap: The problem is too complex. How to Spot it: Check if the problem is too complex or if you need to break it down. How to Avoid it: Always break down complex problems into smaller steps and use the direction chart and BODMAS to solve them.

TIME‑SAVING SHORTCUTS

1. Elimination Trick: If two numbers are given on adjacent faces, you can eliminate one of them by using the direction chart.
2. Diagram Hack: Draw a simple diagram to visualize the adjacent faces and find the hidden numbers.
3. Pattern Recognition: Look for patterns in the given information to find the hidden numbers.

1‑MINUTE RECAP

"Alright, let's recap the strategy for solving Dice Positions. First, draw a direction chart to visualize the adjacent faces. Then, identify the given information and use BODMAS to evaluate any mathematical expressions. Next, find the hidden numbers using the direction chart and given information. Finally, verify the answer by checking the numbers on adjacent faces. Remember to avoid common mistakes like not using the direction chart or not verifying the answer. And don't get trapped by incomplete information or complex problems. With practice and patience, you'll master Dice Positions and crack the exam with confidence."