Honest Little Apps Challenge collections

Pocket Puzzle Arcade · 27 original mini-challenges

Number Bond Choices

27 original arithmetic choice questions with complete working. Nine families contain three cases each for varied practice.

Choose a response. See the reasoning.

Read the facts, pick the answer that best fits the stated goal, then open the explanation. Start with five or browse the full set. There is no timer or personal assessment; the useful part is understanding the choice.

These are original web companion exercises. They are independent of the app; answers and progress do not transfer. All people and records in the scenarios are fictional.

01 / reasoning

Double-share nests case 1

Two fictional nests share 15 counters. The larger nest must hold exactly twice as many as the smaller nest, and all counters must be assigned. How many counters belong in the smaller nest under this two-to-one rule?

Show the worked answer

A. 5

The total represents three equal shares: one for the smaller nest and two for the larger. Each share is 5, so the smaller nest holds 5. Together the nests contain 5+10=15.

Try next: Draw three equal boxes before grouping them into the two nests.

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02 / reasoning

Equal groups with a missing size case 1

There are 3 identical packs containing 24 counters altogether. Every pack contains the same positive whole number of counters, and none remain outside packs. How many counters must be in each pack for the total to match?

Show the worked answer

B. 8

Dividing 24 counters equally among 3 packs gives 8 per pack. Multiplication checks the answer: 3×8=24. The equal-size requirement makes one common pack size necessary rather than permitting unequal allocations.

Try next: Explain the same calculation using repeated addition.

Link to this question

03 / reasoning

Unpacked remainder case 1

Place 17 counters into as many completely filled packs of 5 as possible. A partially filled pack does not count as complete. After making every possible full pack, how many counters remain unpacked on the table?

Show the worked answer

A. 2

3 full packs use 15 counters, leaving 2. The remainder is smaller than 5, so it cannot form another full pack. The number of packs and the number of leftover counters are separate answers.

Try next: Write a multiplication-plus-remainder equation for the starting total.

Link to this question

04 / reasoning

Choose the missing operator case 1

Complete the equation 4 □ 3 = 7. The box must contain exactly one of addition, subtraction or multiplication. Use ordinary whole-number arithmetic in the displayed order, with no parentheses or extra operations. Which operator makes the equation true?

Show the worked answer

A. +

4 + 3 equals 7, so + is the matching operation. Testing the other two permitted operations gives different results. The order matters for subtraction even though addition and multiplication can be reversed.

Try next: Calculate the results of the two rejected operators as a check.

Link to this question

05 / reasoning

Largest two-digit multiple case 1

Use two different cards from 2, 5, 7 to form a two-digit number divisible by five. Each selected card is used once, and a two-digit number cannot begin with zero. What is the largest permitted number that can be formed?

Show the worked answer

B. 75

The largest valid number is 75. A number divisible by five ends in zero or five; choose the largest available different tens digit that respects that ending. Reusing a card or leading with zero is forbidden.

Try next: List all valid two-digit numbers before selecting the maximum.

Link to this question

06 / reasoning

Complete the three-place sum case 1

A three-place number row must total 20. The first place contains 6, and the last contains 7. Exactly one positive whole number belongs in the middle. Which value completes the required row sum without changing either known place?

Show the worked answer

C. 7

The known places contribute 13, leaving 7 to reach 20. The completed row is 6, 7, 7. Adding all three values checks the result and shows why only one middle value can work.

Try next: Rearrange the row and verify that its sum stays the same.

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07 / reasoning

Repeated forward jumps case 1

A number marker begins at 9. It makes 3 equal forward jumps of 4, with no backward movement and no skipped jumps. The starting value is not itself a jump. Which number does the marker land on after the last jump?

Show the worked answer

A. 21

3 jumps add 12 to the starting value 9, producing 21. Counting the start as a completed jump would stop one jump early. A repeated-addition list or multiplication gives the same final landing.

Try next: Write every landing number, excluding the starting position.

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08 / reasoning

Strictly between the markers case 1

Find all whole numbers strictly greater than 10 and strictly less than 20 that are divisible by 3. Endpoints are excluded even if divisible. Which option lists the complete qualifying set in increasing order, without any extra values?

Show the worked answer

B. 12, 15, 18

The qualifying numbers are 12, 15, 18. Each lies inside the open interval and is a multiple of 3. The endpoint wording matters: “strictly” excludes 10 and 20 regardless of divisibility.

Try next: Mark the interval with open endpoint circles and highlight the valid multiples.

Link to this question

09 / reasoning

Find the starting amount case 1

An unknown starting amount gains 5 counters and then loses 2, finishing with 9. No other changes occur, and counters are whole objects. What was the original amount before either event took place? Work backward from the final total.

Show the worked answer

C. 6

Undo the loss first by adding 2 to 9, then undo the gain by subtracting 5. That returns 6. Inverse operations must follow the reverse event order to reconstruct the original amount.

Try next: Check the answer by replaying both events forward.

Link to this question

10 / reasoning

Double-share nests case 2

Two fictional nests share 21 counters. The larger nest must hold exactly twice as many as the smaller nest, and all counters must be assigned. How many counters belong in the smaller nest under this two-to-one rule?

Show the worked answer

A. 7

The total represents three equal shares: one for the smaller nest and two for the larger. Each share is 7, so the smaller nest holds 7. Together the nests contain 7+14=21.

Try next: Draw three equal boxes before grouping them into the two nests.

Link to this question

11 / reasoning

Equal groups with a missing size case 2

There are 4 identical packs containing 36 counters altogether. Every pack contains the same positive whole number of counters, and none remain outside packs. How many counters must be in each pack for the total to match?

Show the worked answer

B. 9

Dividing 36 counters equally among 4 packs gives 9 per pack. Multiplication checks the answer: 4×9=36. The equal-size requirement makes one common pack size necessary rather than permitting unequal allocations.

Try next: Explain the same calculation using repeated addition.

Link to this question

12 / reasoning

Unpacked remainder case 2

Place 22 counters into as many completely filled packs of 6 as possible. A partially filled pack does not count as complete. After making every possible full pack, how many counters remain unpacked on the table?

Show the worked answer

C. 4

3 full packs use 18 counters, leaving 4. The remainder is smaller than 6, so it cannot form another full pack. The number of packs and the number of leftover counters are separate answers.

Try next: Write a multiplication-plus-remainder equation for the starting total.

Link to this question

13 / reasoning

Choose the missing operator case 2

Complete the equation 7 □ 2 = 5. The box must contain exactly one of addition, subtraction or multiplication. Use ordinary whole-number arithmetic in the displayed order, with no parentheses or extra operations. Which operator makes the equation true?

Show the worked answer

A. −

7 − 2 equals 5, so − is the matching operation. Testing the other two permitted operations gives different results. The order matters for subtraction even though addition and multiplication can be reversed.

Try next: Calculate the results of the two rejected operators as a check.

Link to this question

14 / reasoning

Largest two-digit multiple case 2

Use two different cards from 0, 3, 5 to form a two-digit number divisible by five. Each selected card is used once, and a two-digit number cannot begin with zero. What is the largest permitted number that can be formed?

Show the worked answer

B. 50

The largest valid number is 50. A number divisible by five ends in zero or five; choose the largest available different tens digit that respects that ending. Reusing a card or leading with zero is forbidden.

Try next: List all valid two-digit numbers before selecting the maximum.

Link to this question

15 / reasoning

Complete the three-place sum case 2

A three-place number row must total 25. The first place contains 8, and the last contains 9. Exactly one positive whole number belongs in the middle. Which value completes the required row sum without changing either known place?

Show the worked answer

C. 8

The known places contribute 17, leaving 8 to reach 25. The completed row is 8, 8, 9. Adding all three values checks the result and shows why only one middle value can work.

Try next: Rearrange the row and verify that its sum stays the same.

Link to this question

16 / reasoning

Repeated forward jumps case 2

A number marker begins at 14. It makes 2 equal forward jumps of 5, with no backward movement and no skipped jumps. The starting value is not itself a jump. Which number does the marker land on after the last jump?

Show the worked answer

A. 24

2 jumps add 10 to the starting value 14, producing 24. Counting the start as a completed jump would stop one jump early. A repeated-addition list or multiplication gives the same final landing.

Try next: Write every landing number, excluding the starting position.

Link to this question

17 / reasoning

Strictly between the markers case 2

Find all whole numbers strictly greater than 20 and strictly less than 30 that are divisible by 4. Endpoints are excluded even if divisible. Which option lists the complete qualifying set in increasing order, without any extra values?

Show the worked answer

B. 24, 28

The qualifying numbers are 24, 28. Each lies inside the open interval and is a multiple of 4. The endpoint wording matters: “strictly” excludes 20 and 30 regardless of divisibility.

Try next: Mark the interval with open endpoint circles and highlight the valid multiples.

Link to this question

18 / reasoning

Find the starting amount case 2

An unknown starting amount gains 7 counters and then loses 3, finishing with 12. No other changes occur, and counters are whole objects. What was the original amount before either event took place? Work backward from the final total.

Show the worked answer

C. 8

Undo the loss first by adding 3 to 12, then undo the gain by subtracting 7. That returns 8. Inverse operations must follow the reverse event order to reconstruct the original amount.

Try next: Check the answer by replaying both events forward.

Link to this question

19 / reasoning

Double-share nests case 3

Two fictional nests share 27 counters. The larger nest must hold exactly twice as many as the smaller nest, and all counters must be assigned. How many counters belong in the smaller nest under this two-to-one rule?

Show the worked answer

A. 9

The total represents three equal shares: one for the smaller nest and two for the larger. Each share is 9, so the smaller nest holds 9. Together the nests contain 9+18=27.

Try next: Draw three equal boxes before grouping them into the two nests.

Link to this question

20 / reasoning

Equal groups with a missing size case 3

There are 5 identical packs containing 45 counters altogether. Every pack contains the same positive whole number of counters, and none remain outside packs. How many counters must be in each pack for the total to match?

Show the worked answer

B. 9

Dividing 45 counters equally among 5 packs gives 9 per pack. Multiplication checks the answer: 5×9=45. The equal-size requirement makes one common pack size necessary rather than permitting unequal allocations.

Try next: Explain the same calculation using repeated addition.

Link to this question

21 / reasoning

Unpacked remainder case 3

Place 29 counters into as many completely filled packs of 8 as possible. A partially filled pack does not count as complete. After making every possible full pack, how many counters remain unpacked on the table?

Show the worked answer

C. 5

3 full packs use 24 counters, leaving 5. The remainder is smaller than 8, so it cannot form another full pack. The number of packs and the number of leftover counters are separate answers.

Try next: Write a multiplication-plus-remainder equation for the starting total.

Link to this question

22 / reasoning

Choose the missing operator case 3

Complete the equation 9 □ 4 = 36. The box must contain exactly one of addition, subtraction or multiplication. Use ordinary whole-number arithmetic in the displayed order, with no parentheses or extra operations. Which operator makes the equation true?

Show the worked answer

A. ×

9 × 4 equals 36, so × is the matching operation. Testing the other two permitted operations gives different results. The order matters for subtraction even though addition and multiplication can be reversed.

Try next: Calculate the results of the two rejected operators as a check.

Link to this question

23 / reasoning

Largest two-digit multiple case 3

Use two different cards from 1, 5, 8 to form a two-digit number divisible by five. Each selected card is used once, and a two-digit number cannot begin with zero. What is the largest permitted number that can be formed?

Show the worked answer

B. 85

The largest valid number is 85. A number divisible by five ends in zero or five; choose the largest available different tens digit that respects that ending. Reusing a card or leading with zero is forbidden.

Try next: List all valid two-digit numbers before selecting the maximum.

Link to this question

24 / reasoning

Complete the three-place sum case 3

A three-place number row must total 30. The first place contains 9, and the last contains 11. Exactly one positive whole number belongs in the middle. Which value completes the required row sum without changing either known place?

Show the worked answer

C. 10

The known places contribute 20, leaving 10 to reach 30. The completed row is 9, 10, 11. Adding all three values checks the result and shows why only one middle value can work.

Try next: Rearrange the row and verify that its sum stays the same.

Link to this question

25 / reasoning

Repeated forward jumps case 3

A number marker begins at 19. It makes 4 equal forward jumps of 6, with no backward movement and no skipped jumps. The starting value is not itself a jump. Which number does the marker land on after the last jump?

Show the worked answer

A. 43

4 jumps add 24 to the starting value 19, producing 43. Counting the start as a completed jump would stop one jump early. A repeated-addition list or multiplication gives the same final landing.

Try next: Write every landing number, excluding the starting position.

Link to this question

26 / reasoning

Strictly between the markers case 3

Find all whole numbers strictly greater than 30 and strictly less than 40 that are divisible by 6. Endpoints are excluded even if divisible. Which option lists the complete qualifying set in increasing order, without any extra values?

Show the worked answer

B. 36

The qualifying numbers are 36. Each lies inside the open interval and is a multiple of 6. The endpoint wording matters: “strictly” excludes 30 and 40 regardless of divisibility.

Try next: Mark the interval with open endpoint circles and highlight the valid multiples.

Link to this question

27 / reasoning

Find the starting amount case 3

An unknown starting amount gains 9 counters and then loses 4, finishing with 15. No other changes occur, and counters are whole objects. What was the original amount before either event took place? Work backward from the final total.

Show the worked answer

C. 10

Undo the loss first by adding 4 to 15, then undo the gain by subtracting 9. That returns 10. Inverse operations must follow the reverse event order to reconstruct the original amount.

Try next: Check the answer by replaying both events forward.

Link to this question