# Two sand glasses – Brain Teaser

What is the quickest way to time a 9 minute cooking session with two sand-glasses of 4 and 7 minutes respectively?

**Post your answer and calculations below.**

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Before cooking:

Start both timers – run down 4-minute timer and flip it. Run down remaining 3 minutes of the 7-minute timer and flip it. Run down remaining 1 minute of the 4-minute timer and flip it. Run down 4-minute timer – 7-minute timer should now be have 2 minutes remaining. Total setup time = 12 minutes.

Start cooking:

Run down remaining 2 minutes on 7-minute timer, flip it and run down all 7 minutes. Total cooking time = 9 minutes.

T=0: Start both timers.

T=4: When 4m empties, flip it to restart.

T=7: When 7m empties, flip it to restart (there will 1 min left on 4m).

T=8: When 4m empties, flip the 7m which has been running only 1 min.

T=9: When the 7m empties, you have finished your 9 minute cooking session.

Start 1-4 min and 1-7 min at t=0

When 4 minutes expires, begin 4 min timer again, (t=4), 3 minutes remain on 7 minute timer

When 7 min timer expires, begin any timer(t=7); 1 minute remains on 4 minute timer.

When this 4 minutes timer expires (t=8), one minutes has been drawn out of other timer(began at t=7), flip this and when expires in 1 minute, 9 minutes has elapsed in first 9 minutes.

Flip both 4 and 7 timers over.

When 4 finishes, there is 3 left in 7 timer. Flip 4 Again.

When 7 finishes, 4 has 1 minute left.

Now for the 9 minute timing …

Now start with 1 minute left in 4 minute timer. Run to completion

Flip 4 minute timer. Run to completion.

Flip 4 minute timer. Run to completion.

Total time = 7 + 9 = 16 minutes

Seems easy, so there must be an optimization somewhere …

Optimization:

Flip 4 and 7.

When 4 is done, flip again.

When 7 is done — the 4 is divided into 1 and 3.

Flip 4 (to run for 1 minute) and flip 7.

When 4 is done, 7 has 1 minute … flip 7 minute and run to completion to get to 9 minutes time.

Minimum time = 7 + 1 + 1 = 9 minutes

Start both timers. When the 4 minute timer runs out, turn it over. When the 7 minute timer runs out start the cooking session. There will be 1 minute remaining in the 4 minute timer. When the last minute runs out of the four minute timer, turn it over. When it runs out (5 minutes into cooking session) turn it over and let it run out again. Cooking session complete.

Total elapsed time is 16 minutes.

turn 4minute sand glass and 7 minute sandglass at same time. When 4 minute runs out, turn it again. When 7 minute runs out, there is one minute left in the 4 min sandglass, two more lots of 4 minutes = 9 minutes!

Total time = 16 minutes