test_1

1.js

var count = (function() {
	var a = 0;
	return function(){
		var args = Array.prototype.slice.call(arguments[0]);
		if(arguments.length !== 0){
			for (var i = 0, lngth = args.length; i < lngth; i++) {
				a += args[i];
			}
		}
		return a;
	}
}());

function counter(){
	var f = arguments[0],
		arr = Array.prototype.slice.call(arguments, 1);

	return f.call(null, arr);
}

counter(count, 1);
counter(count, 2,3,4);
counter(count, 5,6,7,8);

console.log(counter(count)); // 8*9/2 = 36 profit =)

// №2
function sum(a,b){
	return a+b;
}

function counter(){
	var s = 0;
	counter = function(){
		if(arguments.length){
			var f = arguments[0],
				arr = Array.prototype.slice.call(arguments, 1);

			s += f.apply(null, arr);
			return s;
		}
	}
}
// closure init
counter();
console.log(counter(sum, 1,2));
console.log(counter(sum, 1,2));

// #3
function counter2(){
	var f = arguments[0],
		arr = Array.prototype.slice.call(arguments, 1);

	counter2.cache += f.apply(null, arr);
	return counter2.cache;
}
counter2.cache = 0;

counter2(sum, 1,2)
counter2(sum, 1,2)
console.log(counter2(sum, 1,2));