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Javascript (94 92 87)

n=5;while(n>4){n=0;for(i in a){n+=a[i]*a[i]|0}a=n+""}alert(["H","Unh"][n>1?1:0]+"appy") 

Input is provided by setting a to the number desired.

Javascript (94 92 87 86)

do{n=0;for(i in a){n+=a[i]*a[i]|0}a=n+''}while(n>4);alert(['H','Unh'][n>1?1:0]+'appy') 

Input is provided by setting a to the number desired.

Credits to mellamokb.

Javascript (94 92)

a="13";h="";while(!h){n=0;for(i in a){n+=a[i]*a[i]|0}n==4?h="Unh":n==1?h="H":a=n+""}alert(h+"appy") 

Input is provided by setting a to the number desired.

Javascript (94 92 87)

n=5;while(n>4){n=0;for(i in a){n+=a[i]*a[i]|0}a=n+""}alert(["H","Unh"][n>1?1:0]+"appy") 

Input is provided by setting a to the number desired.

Javascript (94)

h="";while(!h){n=0;for(i in a){n+=a[i]*a[i]||0}n==4?h="Unhappy":n==1?h="Happy":a=n+""}alert(h) 

Input is provided by setting a to the number desired.

Javascript (94 92)

a="13";h="";while(!h){n=0;for(i in a){n+=a[i]*a[i]|0}n==4?h="Unh":n==1?h="H":a=n+""}alert(h+"appy") 

Input is provided by setting a to the number desired.