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?


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
1 0:00 FLIP FLIP
2 0:04 FLIP 3 min left
3 0:07 1 min left FLIP
4 0:08 FLIP (1 min now in top)
5 0:09 EMPTY

Hourglass Problem Solution
Hourglass Problem Solution