Can You Predict the Baby's Hunger?

Riddler Express

As any caretaker can tell you, one challenging part of caring for an infant is interpreting their cry. Are they hungry? Are they tired? Do they need a diaper change?

Suppose you have an infant who naps peacefully for two hours at a time and then wakes up, crying, due to hunger. After eating quickly, the infant plays alone for another hour, and then cries due to tiredness. This cycle repeats several times over the course of a 12-hour day. (Your rock star baby sleeps peacefully 12 hours through the night.)

You’re working in an adjacent room when your partner walks out and hands you the baby monitor. You’ve completely lost track where in the day this happens. You continue working for another 30 minutes, then you hear the baby cry. What’s the probability that your baby is hungry?

Solution

Since the baby naps for 2 and plays for 1 hour, there are at most 3 cycles over the course of a 12-hour day. Since there is an extra 1 hour of playing to complement the long night sleep, that leaves 2 hours for 4 feeding times.

The graph below illustrates an infant's schedule, where the yellow horizontal lines represent when the infant cries.

Answer

Note that there are 8 times the infant cries, $\frac{1}{2}$ for hunger, and $\frac{1}{2}$ for tiredness.

Rohan Lewis

2021.03.14

Code can be found here.