Close the month: the impossible budget

Each expense can stay whole, drop to half, or go. Whole is worth two comfort points, half is worth one, gone is worth none. You win the level when the spending fits the income and the comfort is at or above what the level asks.

There are 100 levels. What grows is not the length of the list, it is how few arrangements still close the month.

Yes, and by construction rather than by luck. Each level is built backwards from an arrangement that already works, and the income and comfort are derived from it. Then every combination is enumerated to count how many others also close the month.

Measured: around 23 arrangements close the month in the first band and fewer than two in the last, where fifteen levels have exactly one answer.

The first version of that table fixed the slack instead of the count, and the difficulty went the wrong way: more expenses mean more combinations, so the number of winning arrangements grew from 300 to 1546 as the levels went up.

No. The month is invented, the numbers point at no real product, and the game never says what you should cut. It only says whether the arithmetic closes.

Because a puzzle that is solved by not eating is not a puzzle. Those two can only drop to half.