6th grade challenge word problems

A free printable sheet of 8 Grade 6 challenge word problems, with a hint for a grown-up under each one and an answer key worked out by Kizupi’s math engine. Press New sheet for another.

By The Kizupi team · Updated November 4, 2026

Grade 6 challenge word problems

Name: ____________________

The mean of 8 numbers is 11. When one more number is added, the mean becomes 12. What number was added?
Hint for a grown-up: What was the total of the first 8 numbers?
Mia, Bo and Tom are on Kizupi’s math league team. Their ages are 12, 11 and 14, but not in that order. Tom is 12. Mia is older than Bo. How old is Mia?
Hint for a grown-up: Tom is 12. Which two ages are left for Mia and Bo?
A round skate track has an inside lane with a radius of 31 m. The outside lane runs 1 m further out, all the way around. How many meters longer is one lap of the outside lane? Use 3.14 for π.
Hint for a grown-up: Find each lap: 2 × 3.14 × radius. What do the two laps have in common?
The math league pizza party has 6 toppings to choose from. Each pizza gets exactly 2 different toppings. How many different pizzas can be made?
Hint for a grown-up: Is a pizza with ham and olives different from a pizza with olives and ham?
The rover counts 3 consecutive whole numbers. They add up to 102. What is the largest of them?
Hint for a grown-up: The numbers are spread evenly. Which one is their mean?
Five survey answers are whole numbers. They have only one mode, 4, a median of 10, a mean of 9 and a range of 11. What is the second largest answer?
Hint for a grown-up: If 4 is the only mode, how many times does it appear? Where do those answers sit in order?
Lily packs 8 shirts, 6 pairs of pants and 5 hats for the island trip. How many different outfits of one shirt, one pair of pants and one hat can Lily make?
Hint for a grown-up: For one shirt, how many shirt-and-pants pairs are there?
The sum of 7 consecutive whole numbers is 147. What is the smallest of them?
Hint for a grown-up: If the numbers are spread evenly, what is their mean?

From kizupi.com/tools · Grade 6, sheet 2110

What these challenge problems cover

Each sheet draws 8 problems from 20 Grade 6 challenge word problems in Kizupi’s published lessons, a different skill for each where it can. Only problems that work on paper are used.

Star puzzle · Counting principles · Combinations · Overlapping sets · Logic and truth-tellers

Where this fits in 6th grade

The Common Core math standards say Grade 6 time should go to these areas [1]:

Ratios and rates
Dividing fractions, and negative numbers
Writing and using expressions and equations
Statistical thinking

For a sheet that mixes every Grade 6 skill, use the 6th grade math word problems page.

Questions parents ask

What are 6th grade challenge word problems?

Puzzle problems a step past the usual ones, where the method isn’t given: working backward, making an organized list, guess and check, or spotting a pattern. These sheets draw from 5 kinds of Grade 6 puzzles in Kizupi: Star puzzle, Counting principles, Combinations, Overlapping sets, Logic and truth-tellers.

Is the worksheet free?

Yes. No account and no email. Press New sheet for another set, and print as many as you like.

Are the answers right?

Every answer is computed with exact arithmetic by the same engine that checks children’s answers in Kizupi, not typed in by hand.

What if my child gets stuck?

That is expected: these are meant to take a while. Read the problem aloud, try it with smaller numbers or a quick drawing, and use the hint under each problem. Save the answer key for the end.

Sources

Common Core State Standards Initiative, Grade 6 introduction. Read October 27, 2026.

Want a tutor that asks “how do you know?” every day? Kizupi’s pixel owl reads each problem aloud, hints one small step at a time and never hands over the answer. Grades 1–6.

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