A climber moves up 5 meters each day but slips back 4 meters each night. If the ledge is 10 meters high, on which day does the climber first reach it?

Day 6. On day 6, the climber reaches 10 meters during the day before slipping back.

Why do problems like 'up by day, down by night' often trick people?

They hide a stopping condition. People forget that once the goal is reached, the sliding back no longer matters.

A snail climbs 3 meters up and slides 2 meters down each day. The wall is 8 meters high. When does it finish?

Day 5. On day 5, it reaches 8 during the climb and is done.

What is the key logical step in solving these problems?

Checking the moment the goal is reached. You must check the daytime position before the nightly slide.

If a robot moves +10 steps forward and −9 backward each cycle, what is its net gain per full cycle?

1. Each full cycle gains exactly 1 step.

Why does the final cycle behave differently from earlier ones?

Because the process ends mid-cycle. The process stops as soon as the target is reached, not after the full cycle.

If a climber gains 2 meters per day but slips 1 meter per night, how many days to reach 6 meters?

5. Day 5 is when it reaches 6 during the climb.

Which mistake leads to the wrong answer in these puzzles?

Counting full cycles only. People count full cycles and forget the partial final day.

A machine advances 8 units and falls back 6 each cycle. How many cycles to first reach 14 units?

7. After 6 cycles it's at 12, on cycle 7 it reaches 14 during the advance.

What does this class of problems mainly test?

Attention to stopping conditions. They test whether you notice when the process stops.

If progress per cycle is positive, what must eventually happen?

It will reach any finite target. Any positive net progress will eventually reach a finite goal.

A frog jumps 4 meters up and slips 3 meters down. The well is 7 meters deep. When does it escape?

Day 3. On day 3, it reaches 7 during the jump and escapes.

Why is averaging the movement per day misleading?

Because the last day is incomplete. The final day does not include the backward movement.

If net gain is 1 per cycle and the target is 10, why is the answer not always 10 cycles?

Because the last cycle is partial. The final cycle ends before the backward step.

A robot moves +6 and −5 each cycle. How many cycles to reach 11?

10. After 9 cycles it's at 9, on cycle 10 it reaches 11 during the move.

What happens if the backward movement is equal to or greater than the forward movement?

It never reaches the goal. If net progress is zero or negative, the goal is never reached.

What is the general strategy to solve these puzzles?

Simulate until just before the final step. You simulate until the last step can reach the goal.

Which real-world situations resemble these puzzles?

Climbing with setbacks. Any progress-with-setback process fits this model.

If a climber gains 7 and loses 2 each cycle, how many cycles to reach 20?

4. After 3 cycles it's at 15, on cycle 4 it reaches 22 and passes 20.

Why do these problems often appear easier than they are?

They hide the final condition. The trick is noticing when the process stops.

If a snail climbs 1 meter and slips 0.5 meters, what matters more: the gain or the loss?

The gain. Only the net positive gain allows eventual progress.

What happens if the target keeps moving upward faster than the climber's net gain?

It never reaches it. If the target moves faster, it can never be reached.

Why is writing a quick formula risky for these puzzles?

You may ignore the last step. Most mistakes come from ignoring the partial final cycle.

What is the simplest way to avoid mistakes in these puzzles?

Simulate step by step. Step-by-step simulation reveals the stopping point.

What is the main lesson of the Daylight Shift puzzles?

Stopping conditions matter more than averages. You must always check when the process actually ends.

QuizKnowledge

The Daylight Shift: A Pattern Recognition Quiz

Test your logic and math skills with the Daylight Shift puzzle variation. Calculate how many days it takes to reach a specific target with daily forward and backward movements.

25 Questions•20 Mins•Medium