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Grade 6 Challenge: Logic & Reasoning Problems Worksheet with Answers

Grade 6 (US) · Year 7 (UK) · Class 6 (India) · Math

Unit 6: Going FurtherChallenge PuzzlesChallenge

Classic reasoning puzzles — ages, heads and legs, consecutive numbers — that reward careful thinking. This free middle school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Logic & Reasoning Problems

Grade 6 · Math

Score___ / 12

Name

Class

Date

Learning goal: Challenge Puzzles

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Three consecutive whole numbers add up to 78. What is the smallest number?

Answer: 25

1
5 people each shake hands once with every other person. How many handshakes are there?
Show your work
Answer
2
A pen and a notebook cost $13 together. The notebook costs $3 more than the pen. How much does the pen cost?
Show your work
Answer
3
A farm has chickens and cows. There are 21 heads and 56 legs. How many cows are there?
Show your work
Answer
4
A farm has chickens and cows. There are 8 heads and 22 legs. How many cows are there?
Show your work
Answer
5
A farm has chickens and cows. There are 12 heads and 34 legs. How many cows are there?
Show your work
Answer
6
9 people each shake hands once with every other person. How many handshakes are there?
Show your work
Answer
7
A farm has chickens and cows. There are 16 heads and 46 legs. How many cows are there?
Show your work
Answer
8
A pen and a notebook cost $20 together. The notebook costs $2 more than the pen. How much does the pen cost?
Show your work
Answer
9
A pen and a notebook cost $10 together. The notebook costs $2 more than the pen. How much does the pen cost?
Show your work
Answer
10
Three consecutive whole numbers add up to 27. What is the smallest number?
Show your work
Answer
11
Three consecutive whole numbers add up to 24. What is the smallest number?
Show your work
Answer
12
A pen and a notebook cost $8 together. The notebook costs $4 more than the pen. How much does the pen cost?
Show your work
Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/6/challenge_logic

Answer key (click to show)

1.10
2.$5
3.7
4.3
5.5
6.36
7.7
8.$9
9.$4
10.8
11.7
12.$2

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How to use this worksheet

Works well as a bell-ringer, exit ticket, homework set or quick quiz.
Have students self-check with the answer key, then correct their own mistakes before you review.
Generate a new version of the same topic for a re-test, so students can't just memorise the answers.

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More Grade 6 Math worksheets

Grade 6 Challenge: Number Theory Puzzles Grade 6 Adding & Subtracting Integers Grade 6 Multiplying & Dividing Integers Grade 6 Integers (Mixed Practice)Grade 6 Two-Step Equations Grade 6 Find the Mistake Grade 6 Bar Model Word Problems Grade 6 Balance Scale Puzzles

Guides for teaching Challenge: Logic & Reasoning Problems

Order of Operations (PEMDAS / BODMAS): Rules, Examples and Common MistakesWhy multiplication doesn't always come before division, how exponents and negatives trip students up, and worked examples you can check.Adding and Subtracting Fractions: A Step-by-Step Guide for Grades 5–6Like and unlike denominators, mixed numbers, and the three mistakes that cause most wrong answers — with worked examples.How to Solve Math Word Problems: A 4-Step MethodRead, plan, solve, check — a simple routine for any word problem, with worked examples and the keyword trap to avoid.

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Frequently asked questions

Does this Grade 6 Challenge: Logic & Reasoning Problems worksheet come with answers?

Yes. The full answer key is on this page, and it prints on its own page after the questions. Every answer is calculated or checked by code rather than written by an AI model, so the key is always correct.

How do I print it or save it as a PDF?

Click "Download PDF" to save a ready-to-print PDF with the answer key on the last page, or click "Print" to send the worksheet and answer key straight to your printer.

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