How can Name-and-form be the cause and condition for the manifestation of the consciousness aggregate? In SN 22.82 Buddha says Name and Form is the cause and condition for the manifestation of Consciousness aggregate.


  “The four great elements, bhikkhu, are the cause and condition for the
  manifestation of the form aggregate. Contact is the cause and
  condition for the manifestation of the feeling aggregate. Contact is
  the cause and condition for the manifestation of the perception
  aggregate. Contact is the cause and condition for the manifestation of
  the volitional formations aggregate. Name-and-form is the cause and
  condition for the manifestation of the consciousness aggregate.”


However while elucidating dependent origination Buddha says Consciousness is the cause and condition for Name and form.


  This being so that is, beginning with the arising of this that arises,
  thus: because of ignorance there are volitional processes, because of
  volitional processes: consciousness, because of consciousness: mind
  and body, because of mind and body: the six sense-spheres, because of
  the six sense-spheres: contact, because of contact: feeling, because
  of feeling: craving, because of craving: attachment, because of
  attachment: continuation, because of continuation: birth, because of
  birth: old age, death, grief, lamentation, pain, sorrow, and despair
  all arise, and so there is an origination of this whole great mass of
  suffering.


My question is : Is this a contradiction ? If not then please explain how?
From the Mahanidana Sutta (DN15):


  "If one is asked, 'From what requisite condition does contact come?'
  one should say, 'Contact comes from name-and-form as its requisite
  condition.'
  
  "If one is asked, 'From what requisite condition does name-and-form
  come?' one should say, 'Name-and-form comes from consciousness as its
  requisite condition.'
  
  "If one is asked, 'From what requisite condition does consciousness
  come?' one should say, 'Consciousness comes from name-and-form as its
  requisite condition.'
  
  "Thus, Ananda, from name-and-form as a requisite condition comes
  consciousness. From consciousness as a requisite condition comes
  name-and-form. From name-and-form as a requisite condition comes
  contact. From contact as a requisite condition comes feeling. From
  feeling as a requisite condition comes craving. From craving as a
  requisite condition comes clinging. From clinging as a requisite
  condition comes becoming. From becoming as a requisite condition comes
  birth. From birth as a requisite condition, aging, death, sorrow,
  lamentation, pain, distress, and despair come into play. Such is the
  origination of this entire mass of stress.


Did you notice the loop?

Piya Tan in his commentary on Dependent Origination, talks about five versions of Dependent Origination in the Pali suttas:


  Roderick S Bucknell (1999) identifies five main variations or versions
  of dependent arising: the standard version(s), the branched
  version, the looped version, the Sn (Sutta nipāta) version and the 
  ancestor of the standard version.
  
  The looped version is so called because it represents consciousness
  and name-and-form as mutually conditioning each other,
   and "this causal loop is confirmed when the series is reiterated in
  summary in the  "normal" or forward direction," thus:
  
  Conditioned by name-and-form is consciousness.
  Conditioned by consciousness is name-and-form.
  Conditioned by name-and-form is contact
  
  The most famous example of the looped version is found in the
  Mahā Nidāna Sutta ; other examples  are  found in the
  Nala, kalapiya Sutta and  the Mahâpadāna Sutta.


The Mahanidana Sutta (DN15) continues in its explanation:


  Name-and-form
  
  "'From consciousness as a requisite condition comes name-and-form.'
  Thus it has been said. And this is the way to understand how from
  consciousness as a requisite condition comes name-and-form. If
  consciousness were not to descend into the mother's womb, would
  name-and-form take shape in the womb?"
  
  "No, lord."
  
  "If, after descending into the womb, consciousness were to depart,
  would name-and-form be produced for this world?"
  
  "No, lord."
  
  "If the consciousness of the young boy or girl were to be cut off,
  would name-and-form ripen, grow, and reach maturity?"
  
  "No, lord."
  
  "Thus this is a cause, this is a reason, this is an origination, this
  is a requisite condition for name-and-form, i.e., consciousness."
  
  Consciousness
  
  "'From name-and-form as a requisite condition comes consciousness.'
  Thus it has been said. And this is the way to understand how from
  name-and-form as a requisite condition comes consciousness. If
  consciousness were not to gain a foothold in name-and-form, would a
  coming-into-play of the origination of birth, aging, death, and stress
  in the future be discerned?
  
  "No, lord."
  
  "Thus this is a cause, this is a reason, this is an origination, this
  is a requisite condition for consciousness, i.e., name-and-form.
  
  "This is the extent to which there is birth, aging, death, passing
  away, and re-arising. This is the extent to which there are means of
  designation, expression, and delineation. This is the extent to which
  the sphere of discernment extends, the extent to which the cycle
  revolves for the manifesting (discernibility) of this world — i.e.,
  name-and-form together with consciousness.


Piya Tan explains this in his same commentary on Dependent Origination:


  However, in the looped versions of Diagram 5b, the nāma-rūpa
  that feeds viññāṇa is what, in Abhidhamma, is called the 
  bhav’aṅga,  the “birth continuum.”  At the moment of dying, this 
  bhav’aṅga is the cuti-citta, “death-consciousness,”
  and is also the  paṭisandhi citta,  “rebirth-consciousness”
  of the next life.
  The modern term for this is the existential consciousness .


So, DN15 says that name-and-form is the condition for consciousness, which is the condition for name-and-form, which is the condition for contact. This is in the looped version of Dependent Origination.

Based on Piya Tan's explanation, the first name-and-form is from the previous life, which is the condition for consciousness. This consciousness, at death, is what the Abhidhamma calls cuti-citta or the "death consciousness" of the previous life, and is the same patisandhi citta or "rebirth consciousness" of the new life. This consciousness, is the requisite condition for the name-and-form of the next life. The second name-and-form is therefore the name-and-form of the next life. This is very clearly proven by the DN15 quote:


  "'From consciousness as a requisite condition comes name-and-form.'
  Thus it has been said. And this is the way to understand how from
  consciousness as a requisite condition comes name-and-form. If
  consciousness were not to descend into the mother's womb, would
  name-and-form take shape in the womb?"
  
  "'From name-and-form as a requisite condition comes consciousness.'
  Thus it has been said. And this is the way to understand how from
  name-and-form as a requisite condition comes consciousness. If
  consciousness were not to gain a foothold in name-and-form, would a
  coming-into-play of the origination of birth, aging, death, and stress
  in the future be discerned?