Reasoning · Grade 2-2 Time Zones and the Calendar

Problem

Convert between clock time systems

The old Joseon clock cuts a day into twelve 2-hour 'hour' units and each of those into 15-minute 'quarter' units. A name is fixed by which 2-hour block a time falls in and how many minutes past that block's start it is. Convert 13:00, 5:30 and 16:00 into these names.
Your answer
How to solve
Strategy Use Matrix Logic — Each conversion is a two-part table lookup: first find which 2-hour 'hour' block the time sits in, then measure how many minutes past that block's start to pick the 'quarter' unit. The two tables act like a grid, so for each time I read down the hour table and across the quarter table. Watching the units (hours into the block, minutes since its start) keeps the two readings straight.
1STEP 1

Convert 13:00

13:00 opens Misi, so 0 minutes in — Misi jeonggak.

13{:}00∈[13{:}00,15{:}00)=Misi, 0 min=Jeonggak
2STEP 2

Convert 5:30

5:30 is 30 minutes into Myosi, which starts at 5:00 — Myosi igak.

5{:}30∈[5{:}00,7{:}00)=Myosi, 5{:}30-5{:}00=30 min=Igak
3STEP 3

Convert 16:00

16:00 is 60 minutes into Sinsi, which starts at 15:00 — Sinsi sagak.

16{:}00∈[15{:}00,17{:}00)=Sinsi, 16{:}00-15{:}00=60 min=Sagak
Answer
13:00 = Misi jeonggak, 5:30 = Myosi igak, 16:00 = Sinsi sagak
Each answer pairs one hour unit with one quarter unit, matching the given examples: 9:00 = Sasi jeonggak confirms 0 minutes = Jeonggak, and 13:15 = Misi ilgak confirms 15 minutes = Ilgak. Our 13:00 = Misi jeonggak agrees with the Misi block and 0 minutes, and 16:00 = Sinsi sagak correctly uses the 60-minute Sagak row that the 120-minute-long block makes possible.
Takeaway

Every old-clock name is just two lookups: which 2-hour block, then how many 15-minute steps in. That is Grade 3 time-reading dressed up in old names!

  • Convert 13:00
  • Convert 5:30
  • Convert 16:00