we love arithmetic don’t we folks. joseph howard invented tŭmni oblatsi as a variant of clouds for their “riyadh” competition, the only logic puzzle-solving contest i’ve entered. of all its puzzles, the tŭmni oblatsi was the one i struggled with the most; i suppose making one of my own could be an attempt to redeem myself. the puzzle below was actually drafted for another contest, though it was off-theme and that contest was eventually canceled anyway. still worth sharing i think.
tŭmni oblatsi rules
place some clouds in the grid. each cloud is a rectangle that is at least two cells wide and at least two cells tall, and no clouds can share an edge or point. each cell in a cloud is labeled with a number from the range given at the bottom-right such that all cells in the same cloud are labeled with the same number, cells in different clouds are labeled with different numbers, and each number from the range is present in a cloud. each number outside of the grid indicates the sum of the numbers along its line of sight into the grid.
“multiples of three or four”