Friday, September 14, 2012

The Sand Clock Puzzle

I recently bought an elegant sand clock and for a few days we were trying to figure out how long does it take for the sand to go all the way down.  Turns out it is around two hours but it appears to change with the room temperature and our lack of patience. Occasionally, sand particles get stuck in the narrow middle passage and then - the time stands still.  Like a globe, sand clock is a great home toy and reminiscence of our rich history.

Apparently sand clocks and water clocks came to replace the shadow (sun) clocks that couldn't work at night. The first water clock was created in Egypt by using a water bucket with a tiny hole in the bottom. As water dripped down, marks were placed on the bucket to mark hour intervals. Soon water clock design evolved into two buckets.  But water clocks had an unexpected flow - they couldn't be used on the ships. Motion of a ship pushed water all around the containers. Someone got an ingenious idea to replace water with sand and such sand clocks became indispensable the 14th century discovery voyages. Story tells that Magellan had 18 sand clocks per ship.

Why did he need more than one?  Perhaps they were of different sand volume and measured different time intervals. Here is a relevant puzzle. Assume Magellan's cook has two sand clocks that measure 7 and 11 minutes. Magellan's favorite fish takes exactly 15 min to be made according to his taste. How can the cook measure 15 min with a 7 and 11 min sand clocks?

Want to make a sand clock at home from two plastic bottles? See these video instructions.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon

Dennis (of Dennis and Katrina) said...

1) Start both clocks.

2) When the 7 minute clock runs out, there will be 4 minutes left in the 11 minute clock. Reset the 7 minute clock.

3) When the 11 minute clock runs out, there will be 3 minutes left on the 7 minute clock. Reset the 11 minute clock.

4) When the 7 minute clcok runs out, there will be 8 minutes left on the 11 minute clock. Start cooking the fish!

5) When the 11 minute clock runs out, 8 minutes have passed. Start the 7 minute clock.

6) When the 7 minute clock runs out, the fish will have been cooking for 15 minutes. Serve it!

Dennis

Flip both the 7min and 11min clocks simultaneously. When the 7min runs out, start cooking the fish. Once the remaining 4 minutes worth of sand pass through the 11min clock, flip it over for a further 11 mins. 4+11 = 15mins as required.

Wang said...

The difference between 7 and 11 is 4 minutes. Therefore, if you flip the 11 and 7 minute sand clocks at the same time, when the 7 minute sand clock ends, you will have 4 minutes left on the 11 minute sand clock.

Start cooking the fish after the 7 minute sand clock finishes and then once the 4 minutes are up in the 11 minute sand clock, flip the 11 minute sand clock so another 11 minutes pass. 11 + 4 = 15 minutes.

Ilya said...

Start both 7 and 11 minutes clocks. When 7 minute clock runs out, flip it. When 11 minute clock runs out, the 7 minute clock has exactly 4 minutes worth of sand in the bottom half. Flip it again. When it runs out, we have 15 minutes total passed from the beginning. Note: this only works with the assumption that sand flows at the same speed regardless of the its amount at the top.

Anonymous said...

Start both the 7 and 11 min. clocks at the same time. When the 7 min. clock finishes, mark where the sand is on the 11 min. clock, turn both clocks over and the 11 min. clock over and it will go for 4 more min., turn the 11 min. clock over and the fish will be done when the sand reaches the 4 min. mark.

Gurubandhu

Jerome said...

I almost hesitate to answer this question. Awhile back, you asked a question similar to this one: ie the 9 minute stake. I think I gave the longest answer in the history of puzzles so this one makes me a little nervous.

The only answer I can come up with is
Step One
========
Start the 11 minute and 7 minute timers together.

Step Two
========
When the 7 minute timer runs out, start to cook. At the same time turn the eleven minute timer over.

Step Three
==========
Let the eleven minute timer run for the 4 minutes it has left in it. Then Turn it over. Let it run for the full 11 minutes.

11 + 4 = 15

Andree said...

Start both clocks together. When the 7 minute clock runs out, put the fish to cook. 4 minutes later, when the 11 minute clock runs out, flip it over for 11 more minutes. 4 + 11 = 15. The fish is cooked for 15 minutes, perfection!

S N said...

Turn both the 7 minute and the 11 minute sand clocks at the same time. Once all the sand from the 7 minute clock has fallen down start cooking the fish. Turn over the 11 minute clock immediately after all the sand in it has fallen. Cook the fish until the last of the sand in the clock falls. The fish would have cooked for 4 + 11 = 15 minutes.

Anonymous said...

Here is my first thought on how the cook could measure 15 minutes for cooking this fish:
(a) Start the 7 minute and 11 minute sand timers at the same time. Right when the 7 minute timer reaches zero, start cooking the fish.
(b) When the 11 minute timer reaches zero (4 minutes into cooking the fish), turn the 11 minute timer over to start it again. When the 11 minute timer reaches zero for the 2nd time, the fish will have been cooking for 15 minutes (11 + 4) and will be ready for Magellan.

This method may not be the most efficient -- it takes 22 minutes for 15 minutes of cooking -- but it works.

TracyZ

Alin Grin said...

You start the two sand clocks togther. When the 7 minutes one ends you turn it around to start another 7 minutes and when the 11 minutes clock is done the 7 minute clock has 3 minutes to go. you turn the 7 minute clock over so it will run for 4 minutes and there you have it 11+4=15.

Annie said...

Start both sand clocks at the same time. When the 7 minute clock is done, start cooking the fish. When the 11 minute clock is done the fish will have cooked for 4 minutes. Turn the 11 minute clock over and stop cooking the fish when the clock is finished. The fish will have cooked for 4 + 11 minutes or 15 minutes.

Larry Krakauer said...

Don't start cooking the fish, but start both timers. When the 7 times out, start the fish - there will be 4 minutes to go on the 11 timer. When it times out, turn it over for 11 more minutes, total 15.

Anonymous said...

The cook turns both the 7 minute sand clock and the 11 minute sand clock over at the same time so that the sand is at the top. When the 7 minute clock has runs down so that the sand is at the bottom, he quickly flips it around. When the 11 minute clock runs down, the 7 minute clock will have 4 minutes worth of sand at the bottom and 3 minutes worth at the top. The cook will then flip the 7 minute clock over so that the 4 minutes of sand that just poured down will again be at the top. When those 4 minutes of sand runs down, it's dinner time!
If the cook doesn't want to cook and flip hourglasses at the same time, he could suggest a newly created dish, sushi.
-mathmover

Jerome said...

I knew I'd make a mistake.

Step one
=======
Set the two timers going together.

Step two
========
When the 7 minute timer is done. Start cooking. Let the 11 minute timer (which has 4 minutes left) drain until it is finished.

Step three
=========
When the 11 minute timer's sand is all gone in the bottom part of the timer, turn it over and let it drain again.

11 + 4 = 15

Solved.

Maria said...

Interesting, there are more answers than I thought. Turns out there are at least three different ways to cook the fish :)

First recipe (a favorite of Ilya, Gurubandhu, Alin, mathmover and Maria):
----------------------------------------------
Start both 7 and 11 minutes clocks and put fish on the pan. When 7 minute clock runs out, flip it. When 11 minute clock runs out, the 7 minute clock has exactly 4 minutes worth of sand in the bottom half. Flip it again. When it runs out, we have 11+4=15 minutes total passed from the beginning. Your fish is ready.

Second recipe (a favorite of Adam T, Wang, Jerome, Andree, S N, TracyZ, Annie and Larry):
----------------------------------------------
Flip both the 7 min and 11 min clocks simultaneously. When the 7 min runs out, start cooking the fish. Once the remaining 4 minutes worth of sand pass through the 11 min clock, flip it over for a further 11 mins. 4+11 = 15 mins as required. Your fish is ready.

Third recipe (a favorite of Dennis):
---------------------------------------
1) Start both clocks.

2) When the 7 minute clock runs out, there will be 4 minutes left in the 11 minute clock. Reset the 7 minute clock.

3) When the 11 minute clock runs out, there will be 3 minutes left on the 7 minute clock. Reset the 11 minute clock.

4) When the 7 minute clcok runs out, there will be 8 minutes left on the 11 minute clock. Start cooking the fish!

5) When the 11 minute clock runs out, 8 minutes have passed. Start the 7 minute clock.

6) When the 7 minute clock runs out, the fish will have been cooking for 15 minutes. Serve it!

So good to see many of our old-time puzzle solvers here. Another puzzle point for everyone. Wang is turning 50 (puzzle points this week) and I hope to catch him for an exclusive interview this week.

Maria said...

Hey Wang - please email me by either replying to one of the newsletters or via the link below. I would love to feature an interview with you in celebration of your 50 puzzle points.