The whole problem-it’s definitely a problem, of the upachaya houses is centered around the philosophy of “growth”, “increase” and “development” or “progressiveness” whatever, which is signified by the 2nd house in a horoscope. When we try to find out the rationale behind the 3rd, 6th, 10th and 11th houses’ being upachaya houses , the simplest method appears to be that of the “bhavatbhavam” principle that is exploring the meaning from house to house. It is a very complicated methodology inherent in much flexibility that to go by this requires sincere attention to the core point of the subject matter. We know that the 2nd house stands for growth. The 2nd from 2nd becomes the 3rd – so we have found the first upachaya. Then count not 2nd, because we are in seach of the next upachaya, that’s why count 3rd from 3rd and we will find the 5th, here only we have to bring in the 2nd count because it is not about the 3rd but of the 2nd as most being significant in a gradual yet direct and genuine growth factor of each of the upachaya houses, this way we find the 6th and when we notice that from the ground of 5th house the 6th jumps to 1oth house – 5th from 6th > 10th, we will be able to discover the last upachaya the 11th house. Naturally the 8th and 12th house being dushana (but they are spiritual moksha trikona too) is considered  to be “apachaya”(decrease), the same way as par general notions the 2nd and 7th houses being so-called maraka houses fall into the same apachaya category. Pandit Gopesh Kumar Ojha suspects the 1st , 4th , and 9th houses’ having been fallen into the same “apachaya” portfolio for they are the auspicious angles and the best trine. But I think I have a solution for him most respectfully that while the 2nd from any house is significant in the “growth” or “increase” factor, the same way the 12th from any house stands for the decrease of that concerened house. By this process as delineated above we will find that the 12th from 2nd is the 1st, the 12th from 5th is the 4th and the 12th from 10th is the 9th and rightfully they might be claimed as being apachaya houses. We have to remind that all the upachaya houses are also ‘Trika” houses. Trika means “triple desires”; tri stands for triple and “ka” means “kama”. So all these houses basically are houses of material desires and greed for worldly possessions, thus malefic planets which are by nature materialistic and possessive will indeed do well in these houses. By the same way the mentioned angles or trine might be deemed to be apachaya in the sense of “materialistic detachment” – this way strong 1st ,4th, and 9th may not bestow upon the native abundant riches but true wisdom and make someone a true seeker of truth. I find it hard to reckon the 10th house as an upachaya house,( and I will not deny that at some points I entertain a healthy disregard to the follies of tradition however cherished and celebrated they be)  it is simply the best angle so far I can comprehend. As this note is just a momentary flash of intuition I would be much obliged if somebody reasonably bring out my missing points and rectify those.