Conundrum # 9 Hourglass Problem

You have two hourglasses. One empties in 7 minutes. The other empties in 4 minutes.

How can you use these two hourglasses to measure exactly 9 minutes?

Suggestion for illustrating the “Hourglass Problem” conundrum

Solution:

Flip both timers over. When the 4-min timer is empty, flip it over (the 7-min timer has 3 minutes left in the top). When the 7-min timer is empty, flip it over (there is now 1 minute left in the top of the 4-min timer). When the 4-min timer is empty for the second time, the 7-min timer has 1 minute worth of sand in the bottom half. Flip it over so there is now 1 minute in the top. When the 7-min timer empties, 9 minutes have elapsed.

Step Elapsed Time 4 Min Timer 7 Min Timer c 0:00 FLIP FLIP d 0:04 FLIP 3 min left e 0:07 1 min left FLIP f 0:08 FLIP (1 min now in top) f 0:09 EMPTY

c d e f g

0:00 0:04 0:07 0:08 0:09

Surfing Scientist | Conundrums © 2004, Ruben Meerman, ABC Science Student Answer Form - Blackline Master

One empties in 7 minutes. One empties in 7 minutes. You have two hourglasses. You have two hourglasses. to measure exactly to measure exactly 9 minutes? to measure exactly 9 minutes? The other empties in 4 minutes. The other empties in 4 minutes. Hourglass Problem Hourglass Problem How canHow you use these two hourglasses canHow you use these two hourglasses Write your name and solution on the back and solution on the Write your name back and solution on the Write your name

One empties in 7 minutes. One empties in 7 minutes. You have two hourglasses. You have two hourglasses. to measure exactly to measure exactly 9 minutes? to measure exactly 9 minutes? The other empties in 4 minutes. The other empties in 4 minutes. Hourglass Problem Hourglass Problem How canHow you use these two hourglasses canHow you use these two hourglasses Write your name and solution on the back and solution on the Write your name back and solution on the Write your name

One empties in 7 minutes. One empties in 7 minutes. You have two hourglasses. You have two hourglasses. to measure exactly to measure exactly 9 minutes? to measure exactly 9 minutes? The other empties in 4 minutes. The other empties in 4 minutes. Hourglass Problem Hourglass Problem How canHow you use these two hourglasses canHow you use these two hourglasses Write your name and solution on the back and solution on the Write your name back and solution on the Write your name

Surfing Scientist | Conundrums © 2004, Ruben Meerman, ABC Science