Here's a different kind of counting problem. Unfortunately, I can't figure out a good way to prevent the player from just filling in the box at the bottom and blocking up the barrels at the top. The idea is to count out the right number of barrels from the top to get the bulldozer across.
Here's my solution: LONOHEV (There are probably better solutions.)
If anyone's interested, here's an updated version using the new fixed blank tile (and slightly less time on the bulldozer). BIXUDYN Most of the existing solutions will still work fine (probably all of them).
HIXELED and NYBEVUC are more like what I had in mind (even though I didn't work it out myself) since they didn't depend on timing to stop the barrels. NYBEVUC might now work because of the closer bulldozer, but it shouldn't be hard to make it run faster.