I just saw your previous reply. Is your kitchen sink along an exterior
wall? It is certainly possible that your kitchen sink pipes have frozen and
not others. If you have no access to the pipes, you are probably better off
just waiting until it gets warmer, instead of trying to troubleshoot a
problem that may be temperature based. Make sure your kitchen faucet is
closed (or better yet, open just a tiny drip) so that you don't get a flood
overflowing the sink when the pipe finally melts.
If your other pipes also pass through areas that might freeze, I would
suggest turning all your faucets (both hot and cold) on just a bit. Even a
tiny trickle should prevent them from freezing.
For the toilet, this is my approach. Take a piece of thin string and tie it
around the overflow pipe to hold it in place. Place a sinker on the other
end of the string. Lift the flapper and put the string under the flapper.
This should allow water to drip out very slowly. When the tank level drops
enough (probably every minute or two), the water will come on to refill the
tank, which will maintain your flow. The sinker will keep the string from
floating up when you flush the toilet, the loop around the overflow will
prevent the sinker and string going down the outflow from the tank.
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