Idle Workshop Decisions

A. 120

The least expensive qualifying combination costs 120 coins. Compare whole bundles plus singles, including combinations that buy an extra machine; the lowest unit price does not eliminate the need to check the final remainder.

Try next: Try finding a second purchase combination and explain why its cost is higher.

B. 10

Upgrading produces 42 coins during 6 working minutes; continuing unchanged produces 32. The difference is 10. The stopped minutes matter even though the upgrade has no purchase cost.

Try next: Change the time window and identify when the pause becomes worthwhile.

C. 34

Regular payouts total 24 coins, and 2 completed bonus intervals add 10. The combined total is 34. An unfinished bonus interval contributes nothing under the stated timing rule.

Try next: Mark the actual bonus minutes on a short timeline.

A. 38

The first visit collects 18 coins; the second collects 20. Together that is 38. Resetting storage between visits matters, while overflow lost before collection cannot be recovered.

Try next: Place a different first collection time and compare the collected total.

B. 15

Reaching the target requires 5 completed batches, delivering 35 tokens. At 3 minutes per batch, the first qualifying time is 15 minutes. Tokens from an unfinished batch cannot count toward the target.

Try next: Find the token total one minute before the successful delivery.

C. Plan B

Plan A costs 48 coins; Plan B costs 46, including its entry fee. Plan B costs less. Compare the full order rather than choosing solely from the per-part prices.

Try next: Calculate the order size at which the two plans would tie.

A. 3

3 purchases cost 45 coins in total, leaving 15. The next purchase costs 25, which exceeds that balance. Adding the changing prices gives the answer; multiplying by the first price would undercount.

Try next: Write the complete price sequence and cross out the first unaffordable upgrade.

B. 46

A runs for 7 minutes and contributes 21; B runs for 5 and contributes 25. Their total is 46. The later start affects B alone, not the machine already running.

Try next: Draw separate operating timelines for the two machines.

C. 3

Only 60 coins are available above the reserve, so 3 modules fit. They leave 31 coins. Another module would break the reserve rule even if the original wallet looked large enough.

Try next: Check the remaining balance after one more module to show why it fails.

A. 210

The least expensive qualifying combination costs 210 coins. Compare whole bundles plus singles, including combinations that buy an extra machine; the lowest unit price does not eliminate the need to check the final remainder.

Try next: Try finding a second purchase combination and explain why its cost is higher.

B. 0

Upgrading produces 54 coins during 6 working minutes; continuing unchanged produces 54. The difference is 0. The stopped minutes matter even though the upgrade has no purchase cost.

Try next: Change the time window and identify when the pause becomes worthwhile.

C. 50

Regular payouts total 36 coins, and 2 completed bonus intervals add 14. The combined total is 50. An unfinished bonus interval contributes nothing under the stated timing rule.

Try next: Mark the actual bonus minutes on a short timeline.

A. 41

The first visit collects 16 coins; the second collects 25. Together that is 41. Resetting storage between visits matters, while overflow lost before collection cannot be recovered.

Try next: Place a different first collection time and compare the collected total.

B. 20

Reaching the target requires 5 completed batches, delivering 45 tokens. At 4 minutes per batch, the first qualifying time is 20 minutes. Tokens from an unfinished batch cannot count toward the target.

Try next: Find the token total one minute before the successful delivery.

C. Plan B

Plan A costs 100 coins; Plan B costs 95, including its entry fee. Plan B costs less. Compare the full order rather than choosing solely from the per-part prices.

Try next: Calculate the order size at which the two plans would tie.

A. 4

4 purchases cost 90 coins in total, leaving 0. The next purchase costs 35, which exceeds that balance. Adding the changing prices gives the answer; multiplying by the first price would undercount.

Try next: Write the complete price sequence and cross out the first unaffordable upgrade.

B. 67

A runs for 8 minutes and contributes 32; B runs for 5 and contributes 35. Their total is 67. The later start affects B alone, not the machine already running.

Try next: Draw separate operating timelines for the two machines.

C. 3

Only 80 coins are available above the reserve, so 3 modules fit. They leave 38 coins. Another module would break the reserve rule even if the original wallet looked large enough.

Try next: Check the remaining balance after one more module to show why it fails.

A. 340

The least expensive qualifying combination costs 340 coins. Compare whole bundles plus singles, including combinations that buy an extra machine; the lowest unit price does not eliminate the need to check the final remainder.

Try next: Try finding a second purchase combination and explain why its cost is higher.

B. 8

Upgrading produces 88 coins during 8 working minutes; continuing unchanged produces 80. The difference is 8. The stopped minutes matter even though the upgrade has no purchase cost.

Try next: Change the time window and identify when the pause becomes worthwhile.

C. 44

Regular payouts total 35 coins, and 3 completed bonus intervals add 9. The combined total is 44. An unfinished bonus interval contributes nothing under the stated timing rule.

Try next: Mark the actual bonus minutes on a short timeline.

A. 57

The first visit collects 30 coins; the second collects 27. Together that is 57. Resetting storage between visits matters, while overflow lost before collection cannot be recovered.

Try next: Place a different first collection time and compare the collected total.

B. 35

Reaching the target requires 7 completed batches, delivering 56 tokens. At 5 minutes per batch, the first qualifying time is 35 minutes. Tokens from an unfinished batch cannot count toward the target.

Try next: Find the token total one minute before the successful delivery.

C. Plan B

Plan A costs 180 coins; Plan B costs 170, including its entry fee. Plan B costs less. Compare the full order rather than choosing solely from the per-part prices.

Try next: Calculate the order size at which the two plans would tie.

A. 4

4 purchases cost 140 coins in total, leaving 10. The next purchase costs 60, which exceeds that balance. Adding the changing prices gives the answer; multiplying by the first price would undercount.

Try next: Write the complete price sequence and cross out the first unaffordable upgrade.

B. 85

A runs for 9 minutes and contributes 45; B runs for 5 and contributes 40. Their total is 85. The later start affects B alone, not the machine already running.

Try next: Draw separate operating timelines for the two machines.

C. 3

Only 105 coins are available above the reserve, so 3 modules fit. They leave 55 coins. Another module would break the reserve rule even if the original wallet looked large enough.

Try next: Check the remaining balance after one more module to show why it fails.