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You can use the -I option of xargs:

Which works in a similar mechanism to find and {}. I would also quote your -name argument (because a file starting with x in the present directory would be file-globed and passed as an argument to find.

Look at Stephane's answer for the best method, take a look at my answer for reasons not to use the more obvious solutions (and reasons why they are not the most efficient).

You can use the -I option of xargs:

Which works in a similar mechanism to find and {}. I would also quote your -name argument (because a file starting with x in the present directory would be file-globed and passed as an argument to find - which will not give the expected behavior!).

Even using the GNU -0 xargs argument and the find -print0 argument causes the -I to  clone() for each file:

Even using the GNU -0 xargs argument and the find -print0 argument causes exactly the same behavior of -I - this is to  clone() a process for each file mv:

However, as pointed out by manatwork, as detailed in the xargs man page:

   -I replace-str
          Replace occurrences of replace-str in the initial-arguments with
          names read from standard input.  Also, unquoted  blanks  do  not
          terminate  input  items;  instead  the  separator is the newline
          character.  Implies -x and -L 1.

The important thing to note is that -L 1 means that only one line of output from find will be processed at a time. This means that's syntactically the same as:

find /tmp/ -ctime -1 -name "x*" -exec mv '{}' ~/play/

(which executes a single mv operation for each file).

Even using the GNU -0 xargs argument and the find -print0 argument causes the -I to clone() for each file:

find . -name "x*" -print0 | strace xargs -0 -I '{}' mv '{}' /tmp/other

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read(0, "./foobar1/xorgslsala11\0./foobar1"..., 4096) = 870
mmap(NULL, 135168, PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANONYMOUS, -1, 0) =     0x7fbb82fad000
open("/usr/lib/x86_64-linux-gnu/gconv/gconv-modules.cache", O_RDONLY) = 3
fstat(3, {st_mode=S_IFREG|0644, st_size=26066, ...}) = 0
mmap(NULL, 26066, PROT_READ, MAP_SHARED, 3, 0) = 0x7fbb82fa6000
close(3)                                = 0
clone(child_stack=0, flags=CLONE_CHILD_CLEARTID|CLONE_CHILD_SETTID|SIGCHLD,         child_tidptr=0x7fbb835af9d0) = 661
wait4(-1, [{WIFEXITED(s) && WEXITSTATUS(s) == 0}], 0, NULL) = 661
--- SIGCHLD (Child exited) @ 0 (0) ---
clone(child_stack=0, flags=CLONE_CHILD_CLEARTID|CLONE_CHILD_SETTID|SIGCHLD,         child_tidptr=0x7fbb835af9d0) = 662
wait4(-1, [{WIFEXITED(s) && WEXITSTATUS(s) == 0}], 0, NULL) = 662
--- SIGCHLD (Child exited) @ 0 (0) ---
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