Question 67089
Wierd---I thought I had solved this one already, but for some reason, I can't find it. Anyway, here's how to do it.

There is only 1 possibility for the first digit of any of the numbers, as no 3-digit number with an even first digit is underneath 300 unless the first digit is 2. Therefore, we take 1 as the first term.

For the second one, it could be 2,4,6, or 8. So there are 4 choices, as there are for the third term too.

{{{1*4*4=16}}}

Therefore, we have 16 counting numbers less than 300 that have all even digits.

If you'd like a list of the numbers:
222
224
226
228
242
244
246
248
262
264
266
268
282
284
286
288

Done. =)
-Zoop