Read the selection rules first. For a two-number sum, subtract one candidate from the target and look for its complement. For three numbers, fix one and solve the remaining two-number problem.
Agree on the rules before searching
In the six exercises below, use addition only and choose exactly the requested number of entries. Each listed entry can be used at most once. You cannot join digits, introduce a new number or change an entry’s sign. Order does not matter: choosing 4 and 9 is the same solution as choosing 9 and 4.
These original website exercises are separate from app levels, and in-app modes can have their own rules. For more number challenges after this page, explore Moocsoft’s Math Riddles / Math Puzzles app using the download buttons above.
Writing the constraints prevents a common mistake: reaching the target correctly with an invalid selection. A four-number sum does not solve a question that asks for exactly two.
Look for the missing complement
Suppose the target is 17 and one available number is 8. Its complement is 17 − 8 = 9. If 9 also appears in the list, you have a two-number solution. Otherwise, test a different candidate.
For the list 3, 6, 8, 11 and target 14, choosing 3 requires 11, so 3 + 11 works. Choosing 6 requires 8, so there is another solution. Do not assume a puzzle has only one answer unless that is stated.
If a complement equals the candidate, check whether two copies are actually available. With just one 7 in the list, 7 + 7 is not allowed under the no-reuse rule.
Questions 1–3: choose exactly two numbers
| Question | Available numbers | Target |
|---|---|---|
| 1 | 2, 5, 8, 11 | 13 |
| 2 | 3, 7, 12, 16 | 19 |
| 3 | 4, 6, 9, 13 | 18 |
Find every valid pair for each target, not just the first pair you notice.
Reveal all valid pairs
1: 2 + 11 and 5 + 8 both make 13. 2: 3 + 16 and 7 + 12 both make 19. 3: there is no valid pair. Although 9 + 9 = 18, the list contains only one 9. The other needed complements—14, 12 and 5—are absent.
A “no solution” result can be correct. Check all possible complements before deciding that the question must contain an error.
Turn a three-number sum into a smaller problem
To choose three numbers, temporarily fix one entry and subtract it from the target. Then search for a pair in the remaining entries. With target 20 and fixed entry 4, you need two other numbers totaling 16.
Keep a simple order, such as testing the smallest chosen entry first. Otherwise you may rediscover the same selection in different orders and count it more than once. For a short list, a written checklist is usually enough.
Because these exercises use only positive numbers, you can also check the smallest and largest allowed totals. If even the three smallest numbers exceed the target, no three-number selection can work. This shortcut would need more care if negative numbers were allowed.
Questions 4–6: choose exactly three numbers
| Question | Available numbers | Target |
|---|---|---|
| 4 | 2, 4, 7, 9 | 15 |
| 5 | 3, 5, 8, 10, 12 | 25 |
| 6 | 1, 4, 6, 9, 11 | 18 |
Reveal all valid selections
4: 2 + 4 + 9 = 15. 5: 3 + 10 + 12 = 25 and 5 + 8 + 12 = 25. 6: 1 + 6 + 11 = 18. Reordering the entries does not create additional selections.
For question 5, fixing 12 leaves a target of 13. Both 3 + 10 and 5 + 8 reach it. To verify that the answer list is complete, also check triples that do not contain 12: none of them totals 25.
Use an answer check that includes the constraints
- Add the selected entries again.
- Count how many entries you used.
- Check that every entry appears in the original list.
- Check that you did not reuse an entry.
- If asked for all answers, remove reordered duplicates and finish your search.
These checks transfer to many number games, but read the rules of each mode before playing. Some games allow other operations; this page deliberately uses addition only.
For a different style of challenge, try missing-number grids or prime-number puzzles. When you want another set on your phone, the app links above take you to the current store versions, including their purchase details.
Common questions
Can a target-sum puzzle have several answers?
Yes. Different selections can reach the same target. Follow the question’s instruction about finding one answer or every answer.
Can I use the same number twice?
Only if the rules permit reuse or the list contains separate copies you are allowed to choose. In this guide, each listed entry can be used once.
What is the quickest first check for a pair?
Subtract a candidate from the target, then check whether the remaining value is available as a different entry.
Published by Moocsoft, the independent studio behind Math Riddles. Examples and worksheets are illustrative. App features can vary by platform and version; see the store listing for current availability and in-app purchases.