The Math of "The Martian" Sol 97 (2)

Sol 97 (2)

Mark has fixed the Pathfinder lander to communicate with earth! Although it will be tedious, the story states that earth and Mars are currently 16 light minutes apart. He can hand write messages on note cards and place them in view of the camera, getting a response is much more tricky. Mark has decided to tell NASA to use ASCII to spell messages. He placed then numbers 0 through 9, and the letters A through F in a circle around the lander. NASA can select one by pointing to the camera at it. The following is their’ first day’s worth of communication:

Mark: Spell with ASCII. 0-F at 21-degree increments. Will watch camera staring 11:00 my time. When message done, return to this position. Wait 20 minutes after completion to take picture (so I can write and post reply). Repeat process at top of every hour.

NASA: STATUS

Mark: No physical problems. All Hab components functional. Eating ¾ rations. Successfully growing crops in Hab with cultivates soil. Note: Situation not Ares 3 crew’s fault. Bad luck.

NASA: HOWALIVE

Mark: Impaled by antenna fragment. Knocked out by decompression. Landed facedown, blood sealed hole. Woke up after crew left. Bio-monitor computer destroyed by puncture. Crew had reason to think me dead. Not their fault.

NASA: CROPS?

Mark: Long story. Extreme botany. Have 126 m2 farmland growing potatoes. Will extend food supply, but not enough to last until Ares 4 landing. Modified rover for long-distance travel, plan to drive to Ares 4.

NASA: WESAW-SATLITE

Mark: Government watching me with satellites? Need tinfoil hat! Also need faster way to communicate. Speak&Spell taking all damn day. Any ideas?

NASA: BRINGSJRNROUT

Mark: Sojourner rover brought out, placed 1 meter due north of lander. If you can concoct it, I can draw hex numbers on the wheels and you can send me six bytes at a time.

NASA: SJRNRNOTRSPND

Mark: Damn. Any other ideas? Need faster communication.

NASA: WORKINGONIT

Mark: Earth is about to set. Resume 08:00 my time tomorrow morning. Tell family I’m fine. Give crew my best. Tell Commander Lewis disco sucks.

How long did this conversation take?

Convert NASA’s transmissions back into ASCII.