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Nine Minutes from Two Hourglasses (illustration)
FILE No.77Unsolved

Nine Minutes from Two Hourglasses

Difficulty ★★☆about 6 minLogic PuzzleHourglassProcedure
With a 7-minute and a 4-minute hourglass, how do you measure 9 minutes?

Case Record

You need to time 9 minutes. You have a 7-minute hourglass and a 4-minute hourglass. You can flip either at any moment.

You follow this procedure:

  1. Flip both at the same time to start.
  2. When the 4-minute one runs out, flip it right away.
  3. When the 7-minute one runs out, flip it right away.
  4. ...
Your question

What is step 4?

Case Files

Evidence

Diagram

Minutes from the startTimeEvent0Start both glasses44-min glass runs out, flip it77-min glass runs out, flip it84-min runs out. 7-min has 1 min of sand fallen9Flip 7-min at 8 -> runs out 1 min later
Diagram

Timeline

  1. Start both.
  2. Flip the 4-minute glass.
  3. Flip the 7-minute glass.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

At minute 7, how much sand is in the bottom of the 7-minute glass after you flip it?

Open hint 2

What about at minute 8?

Open hint 3

How long does it take to run out after flipping then?

Solve It

Your question

What is step 4?

Choose the answer closest to the truth.

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The Truth

At 8 minutes, when the 4-minute one runs out, flip the 7-minute one; when it runs out, 9 minutes have passed

The answer is: at 8 minutes, when the 4-minute one runs out, flip the 7-minute one; when it runs out, 9 minutes have passed.

At 0 start. At 4 the small one runs out; flip it. At 7 the big one runs out; flip it (1 minute of sand is still in the top of the small one). At 8 the small one runs out. The 7-minute glass flipped at 7 has run for 1 minute, so 1 minute of sand is in the bottom. Flip it at 8 and that 1 minute of sand runs through, finishing at 9 minutes.

Flip at minute 8At 7, the 7-minute glass restarts; by 8, 1 minute of sand has fallenFlipping it at 8 sends that 1 minute back through8 + 1 = 9 minutes
Diagram of the solution

Key Points

  • The sand already fallen is the time you can measure next
  • Minute 8 is when the 4-minute glass runs out again
  • Use the leftover 1 minute to reach 9

Why people get fooled

We think a glass must run fully before being flipped.

Similar tricks

  • The sand-difference type
  • The timing-overlap type

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