The Hourglass Puzzle is a neat time-measurement riddle that tests planning and timing. You are given two hourglasses - one runs for 7 minutes, the other for 4 minutes. Your goal is to measure exactly 9 minutes using only these two hourglasses. At first, it looks like you can only measure 4, 7, or sums of those, but with careful flips, you can pinpoint 9 minutes exactly.

This puzzle is popular in brain teasers, interview puzzles, and logic exercises because it forces you to think in overlapping intervals and to use events (when an hourglass empties) as triggers.

Hourglass Puzzle Setup and Rules

Here are the rules of the puzzle:

• You have two hourglasses: one measures 7 minutes, the other 4 minutes.
• You may flip either hourglass at any time, and you may flip them multiple times.
• You cannot pause an hourglass except by flipping it (which reverses the flow).
• Your goal is to measure exactly 9 minutes from the start.
• Use only the two hourglasses and timing of their run-outs to determine when 9 minutes have elapsed.

The challenge: Determine the exact sequence of flips and timings so that you can say “9 minutes have passed” at the correct moment.

How to Solve the Hourglass Puzzle?

The trick is to start both at once and use the moments when one runs out to reset it. By tracking remaining times and flipping at those events, you can produce smaller intervals (1 minute in this puzzle) and combine them to reach 9 minutes exactly.

Below is a reliable, step-by-step method.

Step 1: Start Both Hourglasses Simultaneously

Flip the 7-minute and the 4-minute hourglasses at the same time.

• Time elapsed = 0 minutes.
• Remaining: 7-minute → 7, 4-minute → 4.

Step 2: After 4 Minutes - First Flip

When the 4-minute hourglass runs out, 4 minutes have passed.

• Time elapsed = 4 minutes.
• Remaining in 7-minute = 3 minutes (because 7 − 4 = 3).
  Immediately flip the 4-minute hourglass to restart it.

Step 3: After Next 3 Minutes - Second Flip

Wait until the 7-minute hourglass runs out. That takes 3 more minutes.

• Time elapsed = 4 + 3 = 7 minutes.
• At that moment, the restarted 4-minute hourglass has 1 minute left (because it was restarted at minute 4, so by minute 7 it has run 3 of its 4 minutes).
  Immediately flip the 7-minute hourglass to restart it.

Step 4: Use the 1-Minute Remaining on the 4-Minute Hourglass

Now wait 1 minute, until the 4-minute hourglass runs out again.

• Time elapsed = 7 + 1 = 8 minutes.
• At this point, the 7-minute hourglass - which was restarted at minute 7 - has 6 minutes remaining (7 − 1 = 6).
  Immediately flip the 4-minute hourglass again to restart it.

Step 5: Measure the Final Minute

Now wait 1 more minute - when the 4-minute hourglass runs out this time, exactly 9 minutes will have passed in total (8 + 1 = 9).

• Time elapsed = 9 minutes.
  You have measured exactly 9 minutes using the sequence of flips above.

Visual Step Summary:

Event	Action	Time Elapsed (min)	7-min Remaining	4-min Remaining
Start	Flip both	0	7	4
1	4-min runs out → flip 4-min	4	3	4 (just flipped)
2	7-min runs out → flip 7-min	7	7 (just flipped)	1
3	4-min runs out → flip 4-min	8	6	4 (just flipped)
4	4-min runs out again	9	5	0

Why This Works?

You create a 1-minute interval by exploiting the overlap: when the 7-minute runs out at minute 7, the 4-minute has 1 minute left. Using that 1-minute chunk and restarting the 4-minute gives you a final 1-minute to reach 9. In other words, the interaction of the two durations produces smaller measurable intervals that you can combine to reach the target.

Alternate View (Intervals and Differences)

Think of the two hourglasses as producing times that are linear combinations of 7 and 4. The greatest common divisor (gcd) of 7 and 4 is 1, which means you can represent any integer minute (in principle) as a combination of flips and waits. Practically, you create 1-minute increments by aligning run-out moments, then sum those increments to reach 9.

Final Answer: Exact Sequence to Measure 9 Minutes

1. Flip both hourglasses at time 0.
2. At 4 min, when the 4-minute runs out, flip the 4-minute immediately.
3. At 7 min, when the 7-minute runs out, flip the 7-minute immediately (the 4-minute now has 1 minute left).
4. At 8 min, when the 4-minute runs out, flip the 4-minute immediately.
5. At 9 min, the 4-minute runs out again - exactly 9 minutes have elapsed.

By following these flips and waits, you measure 9 minutes exactly using a 7-minute and a 4-minute hourglass.

Why the Hourglass Puzzle is Popular?

This puzzle is enjoyed because it’s simple to state but not obvious to solve at a glance. It trains:

• Event-based reasoning (act when an hourglass runs out),
• Planning ahead (anticipate remaining times), and
• Using differences between timers to craft new intervals.

It appears often in interview rounds, puzzle collections, and logic training sessions.

Similar Logic Puzzles with Answers

If you liked this puzzle, try these related brain teasers that use timing, parity, or stepwise reasoning:

1. The 100 Prisoners Hat Puzzle - Use parity to guarantee at least 99 survivors.
2. The River Crossing Puzzle (Farmer, Goat, Wolf, Cabbage) - Sequence crossings to avoid predation.
3. Egg Timer Problems - Use multiple timers (e.g., 3- and 5-minute timers) to measure other durations.
4. Hourglass 6- and 11-minute Problems - Use gcd reasoning and flips to measure specific minutes.
5. The Monty Hall Problem - Probability twist requiring counterintuitive switching strategy.