Honest Little Apps Challenge collections

Pocket Puzzle Arcade · 27 original mini-challenges

Route Choice Workshop

27 independent route and resource puzzles with selectable answers. Fictional rules are fully stated; no native mechanics are assumed.

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

Compare complete paths case 1

A fictional network offers two routes to the same exit. Route A has consecutive tolls 3 and 4; Route B has tolls 2 and 6. All tolls add, and no other costs exist. Which route has the lowest total toll?

Show the worked answer

A. Route A

Route A totals 7, while Route B totals 8. Route A is cheaper. Evaluate the entire path: selecting the smallest first toll can overlook a larger toll later in the route.

Try next: Change one toll to make the other route preferable.

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02 / reasoning

Collect before unlocking case 1

The exit requires an amber key. You start without keys. Path A visits a station giving red, then the exit. Path B visits a station giving amber, then the exit. Keys persist, and no exchanges exist. Which path can unlock the exit?

Show the worked answer

B. Path B

Path B supplies the required amber key before reaching the exit. Path A supplies only red, which does not match. Having a key is insufficient when the gate requires a particular key label.

Try next: Explain how the answer would change if the two stations exchanged their keys.

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03 / reasoning

Three-state weather switch case 1

A fictional switch cycles a token through sun→rain→wind→sun. Start with sun, and pass through the switch 2 times. Every pass advances exactly one arrow, with no skipped states. Which token state remains after the final pass?

Show the worked answer

C. wind

After 2 advances, the token is wind. The cycle repeats every three passes, so complete cycles restore the starting state and only the remaining passes change it. The direction of the arrows matters.

Try next: Write the state after every pass to check the cycle.

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04 / reasoning

Respect one-way arrows case 1

The complete directed network contains only these arrows: S→A, A→T, T→B. Start at S and try to reach T. An arrow may be followed only in its displayed direction, and no missing connection may be assumed. Is T reachable?

Show the worked answer

A. Reachable

A directed route from S to T exists. S→A→T uses two available arrows. Reversing an arrow would violate the network rules. Only the explicitly listed directed connections may be used.

Try next: Draw the network and mark every node reachable from S.

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05 / reasoning

Narrowest bridge case 1

A single route crosses three bridges with load limits 8, 5, 7 counters. A traveler must carry the same whole load across every bridge without unloading. A load equal to a limit is allowed. What is the greatest load that can complete the route?

Show the worked answer

B. 5

The route can carry at most 5 counters, the smallest bridge limit. That load fits all three bridges. Any larger load fails at least one bridge, regardless of how generous the other bridge limits are.

Try next: Identify which bridge would reject a load one counter heavier.

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06 / reasoning

Count distinct branch routes case 1

Start S connects separately to A, B. Each of those nodes connects directly to exit T. These are the only arrows, all directed toward T. A route is its ordered node sequence. How many different S-to-T routes exist?

Show the worked answer

C. 2

There are 2 routes, one through each intermediate node. Every route consists of S, one chosen branch, then T. Counting the two arrows within each route separately would double-count routes rather than find additional choices.

Try next: Write every complete route as a three-node sequence.

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07 / reasoning

Survive the first toll case 1

Start with 4 energy. Pay 5 to enter a station, receive 8 there, then pay 2 to exit. Energy cannot become negative at any step, and station energy arrives only after entry. Can this route be completed?

Show the worked answer

A. No

The entry toll exceeds the starting energy, so the station cannot be reached. A later reward cannot pay an earlier unaffordable toll. Every intermediate balance must remain nonnegative throughout the journey.

Try next: Record energy before and after every event, not just the final sum.

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08 / reasoning

Keys that are consumed case 1

A route contains 3 locked gates in a row. Each gate consumes exactly one key when opened, and keys cannot be reused. You start with 2 keys and collect none during travel. Can you open every gate on the route?

Show the worked answer

B. No

The route needs 3 keys but only 2 are available, leaving a shortage of 1. Consumption means one key cannot open multiple gates. Gate order does not change the total key demand.

Try next: Show the key balance immediately after each possible gate.

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09 / reasoning

Avoid the closed station case 1

Three routes are listed: S→A→T, S→B→T and S→C→T. Station A is closed, so a route visiting it is forbidden. Every other listed route is open. Which option gives all the usable routes?

Show the worked answer

C. S→B→T and S→C→T

S→B→T and S→C→T remain usable because neither visits A. Remove the route containing the closed station, but keep the others. Sharing the same start and exit does not make their intermediate stations identical.

Try next: Recheck the usable set after closing a different intermediate station.

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10 / reasoning

Compare complete paths case 2

A fictional network offers two routes to the same exit. Route A has consecutive tolls 5 and 2; Route B has tolls 3 and 3. All tolls add, and no other costs exist. Which route has the lowest total toll?

Show the worked answer

A. Route B

Route A totals 7, while Route B totals 6. Route B is cheaper. Evaluate the entire path: selecting the smallest first toll can overlook a larger toll later in the route.

Try next: Change one toll to make the other route preferable.

Link to this question

11 / reasoning

Collect before unlocking case 2

The exit requires a blue key. You start without keys. Path A collects blue before the exit. Path B reaches the exit first and would collect blue afterward. Keys cannot be borrowed from future stations. Which path can unlock the exit when reached?

Show the worked answer

A. Path A

Path A obtains blue before it is needed. Path B reaches the locked exit while still empty-handed, so its later key cannot help at that moment. Matching key labels are insufficient unless the acquisition occurs before the gate.

Try next: Mark the inventory immediately before the exit on each path.

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12 / reasoning

Three-state weather switch case 2

A fictional switch cycles a token through sun→rain→wind→sun. Start with rain, and pass through the switch 4 times. Every pass advances exactly one arrow, with no skipped states. Which token state remains after the final pass?

Show the worked answer

C. wind

After 4 advances, the token is wind. The cycle repeats every three passes, so complete cycles restore the starting state and only the remaining passes change it. The direction of the arrows matters.

Try next: Write the state after every pass to check the cycle.

Link to this question

13 / reasoning

Respect one-way arrows case 2

The complete directed network contains only these arrows: S→B, B→A, A→T. Start at S and try to reach T. An arrow may be followed only in its displayed direction, and no missing connection may be assumed. Is T reachable?

Show the worked answer

A. Reachable

A directed route from S to T exists. S→B→A→T uses three available arrows. Reversing an arrow would violate the network rules. Only the explicitly listed directed connections may be used.

Try next: Draw the network and mark every node reachable from S.

Link to this question

14 / reasoning

Narrowest bridge case 2

A single route crosses three bridges with load limits 4, 9, 6 counters. A traveler must carry the same whole load across every bridge without unloading. A load equal to a limit is allowed. What is the greatest load that can complete the route?

Show the worked answer

B. 4

The route can carry at most 4 counters, the smallest bridge limit. That load fits all three bridges. Any larger load fails at least one bridge, regardless of how generous the other bridge limits are.

Try next: Identify which bridge would reject a load one counter heavier.

Link to this question

15 / reasoning

Count distinct branch routes case 2

Start S connects separately to A, B, C. Each of those nodes connects directly to exit T. These are the only arrows, all directed toward T. A route is its ordered node sequence. How many different S-to-T routes exist?

Show the worked answer

C. 3

There are 3 routes, one through each intermediate node. Every route consists of S, one chosen branch, then T. Counting the two arrows within each route separately would double-count routes rather than find additional choices.

Try next: Write every complete route as a three-node sequence.

Link to this question

16 / reasoning

Survive the first toll case 2

Start with 6 energy. Pay 4 to enter a station, receive 3 there, then pay 4 to exit. Energy cannot become negative at any step, and station energy arrives only after entry. Can this route be completed?

Show the worked answer

A. Yes

After entry, energy is 2; the station raises it to 5, enough for the 4-energy exit. A later reward cannot pay an earlier unaffordable toll.

Try next: Record energy before and after every event, not just the final sum.

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17 / reasoning

Keys that are consumed case 2

A route contains 2 locked gates in a row. Each gate consumes exactly one key when opened, and keys cannot be reused. You start with 3 keys and collect none during travel. Can you open every gate on the route?

Show the worked answer

B. Yes

There are enough keys: 2 are consumed and 1 remain. Consumption means one key cannot open multiple gates. Gate order does not change the total key demand.

Try next: Show the key balance immediately after each possible gate.

Link to this question

18 / reasoning

Avoid the closed station case 2

Three routes are listed: S→A→T, S→B→T and S→C→T. Station B is closed, so a route visiting it is forbidden. Every other listed route is open. Which option gives all the usable routes?

Show the worked answer

C. S→A→T and S→C→T

S→A→T and S→C→T remain usable because neither visits B. Remove the route containing the closed station, but keep the others. Sharing the same start and exit does not make their intermediate stations identical.

Try next: Recheck the usable set after closing a different intermediate station.

Link to this question

19 / reasoning

Compare complete paths case 3

A fictional network offers two routes to the same exit. Route A has consecutive tolls 2 and 7; Route B has tolls 4 and 5. All tolls add, and no other costs exist. Which route has the lowest total toll?

Show the worked answer

A. Routes tie

Route A totals 9, while Route B totals 9. They therefore tie. Evaluate the entire path: selecting the smallest first toll can overlook a larger toll later in the route.

Try next: Change one toll to make the other route preferable.

Link to this question

20 / reasoning

Collect before unlocking case 3

Two consecutive gates each consume one blue key. Path A collects one blue key before both gates; Path B collects two. No further keys exist, and consumed keys cannot be reused. Which path can open both gates and reach the exit?

Show the worked answer

B. Path B

Path B starts the gates with two keys, leaving one after the first gate and zero after the second. Path A runs out after its first gate. Consumption requires a separate key for each gate.

Try next: Compare this case with gates that return their keys after use.

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21 / reasoning

Three-state weather switch case 3

A fictional switch cycles a token through sun→rain→wind→sun. Start with wind, and pass through the switch 5 times. Every pass advances exactly one arrow, with no skipped states. Which token state remains after the final pass?

Show the worked answer

C. rain

After 5 advances, the token is rain. The cycle repeats every three passes, so complete cycles restore the starting state and only the remaining passes change it. The direction of the arrows matters.

Try next: Write the state after every pass to check the cycle.

Link to this question

22 / reasoning

Respect one-way arrows case 3

The complete directed network contains only these arrows: A→S, S→B, T→B. Start at S and try to reach T. An arrow may be followed only in its displayed direction, and no missing connection may be assumed. Is T reachable?

Show the worked answer

A. Unreachable

No directed route from S reaches T. S reaches B, but B has no outgoing arrow. Reversing an arrow would violate the network rules. Only the explicitly listed directed connections may be used.

Try next: Draw the network and mark every node reachable from S.

Link to this question

23 / reasoning

Narrowest bridge case 3

A single route crosses three bridges with load limits 10, 12, 8 counters. A traveler must carry the same whole load across every bridge without unloading. A load equal to a limit is allowed. What is the greatest load that can complete the route?

Show the worked answer

B. 8

The route can carry at most 8 counters, the smallest bridge limit. That load fits all three bridges. Any larger load fails at least one bridge, regardless of how generous the other bridge limits are.

Try next: Identify which bridge would reject a load one counter heavier.

Link to this question

24 / reasoning

Count distinct branch routes case 3

Start S connects separately to A, B, C, D. Each of those nodes connects directly to exit T. These are the only arrows, all directed toward T. A route is its ordered node sequence. How many different S-to-T routes exist?

Show the worked answer

C. 4

There are 4 routes, one through each intermediate node. Every route consists of S, one chosen branch, then T. Counting the two arrows within each route separately would double-count routes rather than find additional choices.

Try next: Write every complete route as a three-node sequence.

Link to this question

25 / reasoning

Survive the first toll case 3

Start with 8 energy. Pay 9 to enter a station, receive 12 there, then pay 3 to exit. Energy cannot become negative at any step, and station energy arrives only after entry. Can this route be completed?

Show the worked answer

A. No

The entry toll exceeds the starting energy, so the station cannot be reached. A later reward cannot pay an earlier unaffordable toll. Every intermediate balance must remain nonnegative throughout the journey.

Try next: Record energy before and after every event, not just the final sum.

Link to this question

26 / reasoning

Keys that are consumed case 3

A route contains 4 locked gates in a row. Each gate consumes exactly one key when opened, and keys cannot be reused. You start with 4 keys and collect none during travel. Can you open every gate on the route?

Show the worked answer

B. Yes

There are enough keys: 4 are consumed and 0 remain. Consumption means one key cannot open multiple gates. Gate order does not change the total key demand.

Try next: Show the key balance immediately after each possible gate.

Link to this question

27 / reasoning

Avoid the closed station case 3

Three routes are listed: S→A→T, S→B→T and S→C→T. Station C is closed, so a route visiting it is forbidden. Every other listed route is open. Which option gives all the usable routes?

Show the worked answer

C. S→A→T and S→B→T

S→A→T and S→B→T remain usable because neither visits C. Remove the route containing the closed station, but keep the others. Sharing the same start and exit does not make their intermediate stations identical.

Try next: Recheck the usable set after closing a different intermediate station.

Link to this question