Honest Little Apps Challenge collections

Pocket Puzzle Arcade · 27 original mini-challenges

Island Transfer Decisions

27 original island-number questions with worked solutions. Transfers, costs and target conditions are explicit independent web rules.

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

Simultaneous island flows case 1

Islands A, B and C begin with 12, 4 and 3 counters. Simultaneously, A sends 3 to B and B sends 2 to C. Each has enough starting counters for its outgoing transfer. What is B’s new total after both transfers settle?

Show the worked answer

A. 5

B receives 3 and sends 2, so its new total is 4+3−2=5. Both changes affect the same island. Counting only incoming or only outgoing counters omits part of the simultaneous update.

Try next: Compute A and C afterward and check the conserved overall total.

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02 / reasoning

Island ledger case 1

An island begins with 8 counters. During a complete round it receives 5 counters from neighboring islands and sends out 3. No counters are created, lost or returned within that round. What ending balance should its ledger record?

Show the worked answer

B. 10

The ending balance is 8+5−3=10. Incoming transfers increase the island’s stock, and outgoing transfers decrease it. Their signs differ even though both kinds of movement cross a bridge connected to the island.

Try next: Write the same ledger as starting balance plus net inflow.

Link to this question

03 / reasoning

Two-at-a-time bridge case 1

An island begins with 3 counters. Its only allowed change is receiving exactly two counters per bridge crossing, with unlimited donor supply. No removals or smaller transfers are allowed. Can the island reach exactly 10 counters after some whole number of crossings?

Show the worked answer

C. No

Each crossing preserves whether the island total is odd or even. The required increase is 7, which is not divisible by two. Therefore the exact target cannot be reached using only two-counter additions.

Try next: List the first four reachable totals to reveal the parity pattern.

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04 / reasoning

Match the route total case 1

Route A visits islands labeled 2 and 5; Route B visits islands labeled 3 and 4. A route’s score is the sum of its two labels. The required score is exactly 7. Which listed routes satisfy the target?

Show the worked answer

A. Both routes

Route A totals 7; Route B totals 7. Comparing each total with the exact target 7 gives both routes. A larger score is not automatically better because the task requires equality, not a minimum threshold.

Try next: Change the target to make a different route outcome correct.

Link to this question

05 / reasoning

Unequal target islands case 1

A begins with 12 counters and B with 2. Their targets are A=8 and B=6; equal totals are not required. Only transfers from A to B are allowed. How many counters must cross to satisfy both targets simultaneously?

Show the worked answer

B. 4

A must send 12−8=4, and B needs 6−2=4. The matching requirements show one transfer satisfies both. Equalizing the islands would answer a different question because these targets are deliberately unequal.

Try next: Verify conservation by comparing starting and target combined totals.

Link to this question

06 / reasoning

Counters spent at each crossing case 1

A traveler carries 9 counters across 2 bridges. Each crossing consumes 1 counters as a toll, permanently removing them from the carried load. No counters are gained elsewhere. How many counters remain with the traveler after all required crossings?

Show the worked answer

C. 7

2 tolls consume 2 counters, leaving 9−2=7. The toll repeats at every bridge rather than being charged once for the entire route. These counters are spent, so carried totals are not conserved.

Try next: Record the carried load immediately after every crossing.

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07 / reasoning

Partial return ledger case 1

An island starts with 7 counters and sends 4 to a neighbor. Later the neighbor returns 1 of those counters, with no other traffic. How many counters does the original island hold after the return is complete?

Show the worked answer

A. 4

The island first falls to 3, then the return adds 1, giving 4. Only the returned amount comes back; the original outgoing transfer is not completely reversed. Tracking the two events separately avoids changing the wrong sign.

Try next: Calculate how many of the originally sent counters remain with the neighbor.

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08 / reasoning

Missing incoming bridge case 1

An island starts with 6 counters, receives 3 through one bridge, receives an unknown amount through another, and sends 4 away. It finishes with 10. No other changes occur. How many counters arrived through the unknown incoming bridge?

Show the worked answer

B. 5

The known changes would leave 5, so the missing inflow must add 5 to reach 10. Substituting 5 gives 6+3+5−4=10. The unknown transfer is incoming, so it increases the balance.

Try next: Solve the same equation by moving the known terms to the other side.

Link to this question

09 / reasoning

Optional bridges used once case 1

An empty island may receive 2 counters from bridge A and 5 from bridge B. Each bridge can be used at most once, and either may be skipped. Transfers cannot be split. Can the island finish with exactly 7 counters?

Show the worked answer

C. Yes

The possible totals are 0, 2, 5, 7: use neither bridge, either one, or both. 7 appears in that list, so the target is reachable. Reordering the same chosen transfers does not change their sum.

Try next: List the bridge choices beside their corresponding final totals.

Link to this question

10 / reasoning

Simultaneous island flows case 2

Islands A, B and C begin with 15, 6 and 5 counters. Simultaneously, A sends 4 to B and B sends 3 to C. Each has enough starting counters for its outgoing transfer. What is B’s new total after both transfers settle?

Show the worked answer

A. 7

B receives 4 and sends 3, so its new total is 6+4−3=7. Both changes affect the same island. Counting only incoming or only outgoing counters omits part of the simultaneous update.

Try next: Compute A and C afterward and check the conserved overall total.

Link to this question

11 / reasoning

Island ledger case 2

An island begins with 11 counters. During a complete round it receives 7 counters from neighboring islands and sends out 6. No counters are created, lost or returned within that round. What ending balance should its ledger record?

Show the worked answer

B. 12

The ending balance is 11+7−6=12. Incoming transfers increase the island’s stock, and outgoing transfers decrease it. Their signs differ even though both kinds of movement cross a bridge connected to the island.

Try next: Write the same ledger as starting balance plus net inflow.

Link to this question

12 / reasoning

Two-at-a-time bridge case 2

An island begins with 4 counters. Its only allowed change is receiving exactly two counters per bridge crossing, with unlimited donor supply. No removals or smaller transfers are allowed. Can the island reach exactly 12 counters after some whole number of crossings?

Show the worked answer

C. Yes

Each crossing preserves whether the island total is odd or even. The required increase is 8, which is divisible by two. Therefore the exact target can be reached using only two-counter additions.

Try next: List the first four reachable totals to reveal the parity pattern.

Link to this question

13 / reasoning

Match the route total case 2

Route A visits islands labeled 4 and 1; Route B visits islands labeled 6 and 2. A route’s score is the sum of its two labels. The required score is exactly 8. Which listed routes satisfy the target?

Show the worked answer

A. Route B

Route A totals 5; Route B totals 8. Comparing each total with the exact target 8 gives route b. A larger score is not automatically better because the task requires equality, not a minimum threshold.

Try next: Change the target to make a different route outcome correct.

Link to this question

14 / reasoning

Unequal target islands case 2

A begins with 16 counters and B with 4. Their targets are A=11 and B=9; equal totals are not required. Only transfers from A to B are allowed. How many counters must cross to satisfy both targets simultaneously?

Show the worked answer

B. 5

A must send 16−11=5, and B needs 9−4=5. The matching requirements show one transfer satisfies both. Equalizing the islands would answer a different question because these targets are deliberately unequal.

Try next: Verify conservation by comparing starting and target combined totals.

Link to this question

15 / reasoning

Counters spent at each crossing case 2

A traveler carries 12 counters across 3 bridges. Each crossing consumes 2 counters as a toll, permanently removing them from the carried load. No counters are gained elsewhere. How many counters remain with the traveler after all required crossings?

Show the worked answer

C. 6

3 tolls consume 6 counters, leaving 12−6=6. The toll repeats at every bridge rather than being charged once for the entire route. These counters are spent, so carried totals are not conserved.

Try next: Record the carried load immediately after every crossing.

Link to this question

16 / reasoning

Partial return ledger case 2

An island starts with 10 counters and sends 6 to a neighbor. Later the neighbor returns 2 of those counters, with no other traffic. How many counters does the original island hold after the return is complete?

Show the worked answer

A. 6

The island first falls to 4, then the return adds 2, giving 6. Only the returned amount comes back; the original outgoing transfer is not completely reversed. Tracking the two events separately avoids changing the wrong sign.

Try next: Calculate how many of the originally sent counters remain with the neighbor.

Link to this question

17 / reasoning

Missing incoming bridge case 2

An island starts with 9 counters, receives 5 through one bridge, receives an unknown amount through another, and sends 6 away. It finishes with 14. No other changes occur. How many counters arrived through the unknown incoming bridge?

Show the worked answer

B. 6

The known changes would leave 8, so the missing inflow must add 6 to reach 14. Substituting 6 gives 9+5+6−6=14. The unknown transfer is incoming, so it increases the balance.

Try next: Solve the same equation by moving the known terms to the other side.

Link to this question

18 / reasoning

Optional bridges used once case 2

An empty island may receive 3 counters from bridge A and 7 from bridge B. Each bridge can be used at most once, and either may be skipped. Transfers cannot be split. Can the island finish with exactly 6 counters?

Show the worked answer

C. No

The possible totals are 0, 3, 7, 10: use neither bridge, either one, or both. 6 does not appear in that list, so the target is not reachable. Reordering the same chosen transfers does not change their sum.

Try next: List the bridge choices beside their corresponding final totals.

Link to this question

19 / reasoning

Simultaneous island flows case 3

Islands A, B and C begin with 18, 8 and 7 counters. Simultaneously, A sends 5 to B and B sends 4 to C. Each has enough starting counters for its outgoing transfer. What is B’s new total after both transfers settle?

Show the worked answer

A. 9

B receives 5 and sends 4, so its new total is 8+5−4=9. Both changes affect the same island. Counting only incoming or only outgoing counters omits part of the simultaneous update.

Try next: Compute A and C afterward and check the conserved overall total.

Link to this question

20 / reasoning

Island ledger case 3

An island begins with 14 counters. During a complete round it receives 9 counters from neighboring islands and sends out 8. No counters are created, lost or returned within that round. What ending balance should its ledger record?

Show the worked answer

B. 15

The ending balance is 14+9−8=15. Incoming transfers increase the island’s stock, and outgoing transfers decrease it. Their signs differ even though both kinds of movement cross a bridge connected to the island.

Try next: Write the same ledger as starting balance plus net inflow.

Link to this question

21 / reasoning

Two-at-a-time bridge case 3

An island begins with 5 counters. Its only allowed change is receiving exactly two counters per bridge crossing, with unlimited donor supply. No removals or smaller transfers are allowed. Can the island reach exactly 14 counters after some whole number of crossings?

Show the worked answer

C. No

Each crossing preserves whether the island total is odd or even. The required increase is 9, which is not divisible by two. Therefore the exact target cannot be reached using only two-counter additions.

Try next: List the first four reachable totals to reveal the parity pattern.

Link to this question

22 / reasoning

Match the route total case 3

Route A visits islands labeled 3 and 7; Route B visits islands labeled 2 and 5. A route’s score is the sum of its two labels. The required score is exactly 10. Which listed routes satisfy the target?

Show the worked answer

A. Route A

Route A totals 10; Route B totals 7. Comparing each total with the exact target 10 gives route a. A larger score is not automatically better because the task requires equality, not a minimum threshold.

Try next: Change the target to make a different route outcome correct.

Link to this question

23 / reasoning

Unequal target islands case 3

A begins with 20 counters and B with 6. Their targets are A=15 and B=11; equal totals are not required. Only transfers from A to B are allowed. How many counters must cross to satisfy both targets simultaneously?

Show the worked answer

B. 5

A must send 20−15=5, and B needs 11−6=5. The matching requirements show one transfer satisfies both. Equalizing the islands would answer a different question because these targets are deliberately unequal.

Try next: Verify conservation by comparing starting and target combined totals.

Link to this question

24 / reasoning

Counters spent at each crossing case 3

A traveler carries 15 counters across 2 bridges. Each crossing consumes 3 counters as a toll, permanently removing them from the carried load. No counters are gained elsewhere. How many counters remain with the traveler after all required crossings?

Show the worked answer

C. 9

2 tolls consume 6 counters, leaving 15−6=9. The toll repeats at every bridge rather than being charged once for the entire route. These counters are spent, so carried totals are not conserved.

Try next: Record the carried load immediately after every crossing.

Link to this question

25 / reasoning

Partial return ledger case 3

An island starts with 13 counters and sends 8 to a neighbor. Later the neighbor returns 3 of those counters, with no other traffic. How many counters does the original island hold after the return is complete?

Show the worked answer

A. 8

The island first falls to 5, then the return adds 3, giving 8. Only the returned amount comes back; the original outgoing transfer is not completely reversed. Tracking the two events separately avoids changing the wrong sign.

Try next: Calculate how many of the originally sent counters remain with the neighbor.

Link to this question

26 / reasoning

Missing incoming bridge case 3

An island starts with 12 counters, receives 7 through one bridge, receives an unknown amount through another, and sends 8 away. It finishes with 18. No other changes occur. How many counters arrived through the unknown incoming bridge?

Show the worked answer

B. 7

The known changes would leave 11, so the missing inflow must add 7 to reach 18. Substituting 7 gives 12+7+7−8=18. The unknown transfer is incoming, so it increases the balance.

Try next: Solve the same equation by moving the known terms to the other side.

Link to this question

27 / reasoning

Optional bridges used once case 3

An empty island may receive 4 counters from bridge A and 9 from bridge B. Each bridge can be used at most once, and either may be skipped. Transfers cannot be split. Can the island finish with exactly 9 counters?

Show the worked answer

C. Yes

The possible totals are 0, 4, 9, 13: use neither bridge, either one, or both. 9 appears in that list, so the target is reachable. Reordering the same chosen transfers does not change their sum.

Try next: List the bridge choices beside their corresponding final totals.

Link to this question