# The Mystery of the Three Numbers

![Figure 1: A clear, friendly illustration for a worksheet about Addition and subtraction within 100, showing the objects and situation the exercises](https://goa-cc-uat-aili-app-001.azurewebsites.net/api/generate/40235533-91ce-4e83-be8b-9f84d58141ac/asset/920)

This brain teaser asks you to find three numbers that add up to a mystery total. You will use addition strategies and think about how a sum can be made in different ways ([Understanding](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29847)). The puzzle works with numbers up to 100 ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)) and helps you practise composing sums by choosing addends carefully ([Skills](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29848)).

## The puzzle

Three numbers add up to 50.

The first number is 15.

The second number is 5 more than the first number.

What is the third number?

## Hints

**Hint 1:** Start by finding the second number. It is 5 more than 15. What do you get?

**Hint 2:** Now add the first number and the second number together. What is 15 + 20? Then think about what you need to add to reach 50.

**Hint 3:** You have 15 + 20 = 35. How much more do you need to make 50? Try counting up from 35 to 50.

## Answer key

**The answer is 15.**

**The reasoning:**

The first number is 15.

The second number is 5 more than 15, so it is 20.

Now add: 15 + 20 = 35.

To reach 50, you need 50 − 35 = 15.

The three numbers are 15, 20, and 15.

Check: 15 + 20 + 15 = 50. ✓

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*AILI game · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id 40235533-91ce-4e83-be8b-9f84d58141ac*

### Sources

- node:n1: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29843)
- node:n2: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)
- node:n3: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29846)
- node:n4: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29848)
- node:n5: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29847)
- node:n6: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29850)
- node:n7: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29852)
- node:n8: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29851)
- node:n9: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29852)
- node:n10: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29850)
- node:n11: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29848)
- node:n12: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)
- node:n13: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29847)
- node:n14: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29851)
- node:n15: Mathematics › Mathematics (K–6) › Grade 2 › Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. › How can addition and subtraction be interpreted? › Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29846)
- resource:r1: Resources › type#activity, type#classroomactivity › MAT2, MAT3, MAT4, MAT5 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/zcsdujXlaUa2uuq1-kBv0Q)