Host A wants to send something to Host B who is in a different network. Between them is Router 1. Host A sends an ARP broadcast but Router 1 is not answering it. Why is that so?

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    Not sure what you mean. Host A would ARP to find the MAC of Router 1 and the router would reply. Host A could then encapsulate the frame and forward it towards the router. Are you saying if Host A sends a broadcast in its subnet why the router does not forward that to Host B?
    – Daniel Dib
    Dec 2 '13 at 17:56
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    if you truly have host a and host b in different networks, could you check their netmasks? It sounds like the netmask on host a is wrong
    – This
    Dec 2 '13 at 18:27

The router will not do this by default, unless you enable Proxy ARP on that router's interface(s), but best practices dictate Proxy ARP should be disabled wherever possible.

However, host A should know by analyzing its own subnet mask (binary AND against its own subnet mask and Host B's address) that Host B is on a different network, and instead send the traffic to its default gateway (if one is configured), and if necessary, Host A will ARP for its default gateway's MAC address, which the router should respond to when appropriate.

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