function rnd(a,b) {
	return a + Math.floor(Math.random()*(b-a+1));
}

function rndz(a,b) {
	var x;
	do {
		x=rnd(a,b);
	} while ( x==0);
	return x;
}

function hcf(a,b) {
	var c;
	while ( b!=0 ) {
		c = a%b; a=b; b=c; 
	}
	return a;
}

function q1(){
	var a = rnd(1,3);
	var b = a + rnd(1,3);
	var c = b + rnd(1,3);
	var d = c + rnd(1,3);
	var e = d + rnd(1,3);
	ans = (a+b+c+d+e)/5;
	qstr+="Find the mean of the numbers: " + a + ", " + b + ", " + c;
	qstr+=", " + d + ", " + e + ".";
	hint+="To calculate the mean, you need to add all the numbers together ";
	hint+="and then divide by the number of numbers.";
}
 
function q2(){
	var a = rnd(1,3);
	var b = a + rnd(1,3);
	var c = b + rnd(1,3);
	var d = c + rnd(1,3);
	var e = d + rnd(1,3);
	var f = e + rnd(1,3);
	ans = (a+b+c+d+e+f)/6;
	ans=Math.round(ans*100)/100;
	qstr+="Find the mean of the numbers: " + a + ", " + b + ", " + c;
	qstr+=", " + d + ", " + e + ", " + f + ".";
	qstr+="<br>Give your answer correct to 2 decimal places.";
	hint+="To calculate the mean, you need to add all the numbers together ";
	hint+="and then divide by the number of numbers.";
}

function q3(){
	var a = rnd(1,3);
	var b = a + rnd(1,3);
	var c = b + rnd(1,3);
	var d = c + rnd(1,3);
	var e = d + rnd(1,3);
	ans = c;
	qstr+="Find the median of the numbers: " + a + ", " + b + ", " + c;
	qstr+=", " + d + ", " + e + ".";
	hint+="To calculate the median, you need to find the middle number when the numbers ";
	hint+="are in increasing order.";
}

function q4(){
	var a = rnd(1,3);
	var b = a + rnd(1,3);
	var c = b + rnd(1,3);
	var d = c + rnd(1,3);
	var e = d + rnd(1,3);
	var f = e + rnd(1,3);
	ans = (c+d)/2;
	qstr+="Find the median of the numbers: " + a + ", " + b + ", " + c;
	qstr+=", " + d + ", " + e + ", " + f + ".";
	hint+="To calculate the median, you need to find the middle number when the numbers ";
	hint+="are in increasing order. When there are an even number of numbers, you need to ";
	hint+="find the average of the <i>two</i> middle numbers.";
}

function q5() {
	var a = rnd(1,4);
	var b = 6-a;
	ans=b+"/6";
	qstr+="If a single six-sided die is rolled once, what is the probability of getting ";
	qstr+="<br>a score greater than " + a + "?";
	qstr+="<br>Give your answer as a fraction.";
	hint+="There are " + b + " ways a die can give a score greater than " + a + ".";
}

function q6(){
	var a=rnd(2,12);
	if (a<8) b=a-1;
	else b=13-a;
	ans=b+"/36";
	qstr+="If two six-sided dice are rolled together, find the probability ";
	qstr+="that the total score is " + a + ".";
	qstr+="<br>Give your answer as a fraction.";
	hint+="Draw a diagram (6x6) to represent the 36 possible outcomes,";
	hint+="<br>then count those that give a total score of " + a + ".";
}

function q7(){
	var a = rnd(8,12);
	var b = rnd(10,20);
	ans = a*b;
	qstr+="If the mean of " + a + " test scores is " + b + ", what is the total ";
	qstr+="of the " + a + " scores?";
	hint+="Since MEAN = TOTAL / NUMBER, we have TOTAL = MEAN x NUMBER.";
}

function q8(){
	var a = rnd(9,10);
	var b = rnd(10,20);
	var c = b + rnd(2,8);
	ans = (a*b+c)/(a+1);
	ans = Math.round(ans*100)/100;
	qstr+="After taking " + a + " tests, my mean score is " + b;
	qstr+="<br>In the next test my score is " + c + ". What is my new mean score?";
	qstr+="<br>Give your answer correct to 2 decimal places.";
	hint+="First work out my total score after " + a + " tests,";
	hint+="<br>then add my next score, and finally divide by " + eval(a+1);
}

function q9(){
	var a=new Array();
	for (var i=1; i<=7; i++ ) a[i]=rnd(3,20);
	var b=3;
	var c=20;
	for (i=1; i<=7; i++ ) {
		if (a[i]>b) b=a[i];
		if (a[i]<c) c=a[i];
	}
	ans=b-c;
	qstr+="Find the range of the following sample:<br><br><center>";
	for (i=1; i<=7; i++ ) qstr+=a[i] + ", ";
	qstr+="</center>";
	hint+="The range is the difference between the largest and smallest numbers in the sample.";
}

function q10(){
	var a=rnd(1,3);
	if (a==1) ans="7/8";
	if (a==2) ans="4/8";
	if (a==3) ans="1/8";
	qstr+="If an unbiased coin is tossed 3 times, find the probability that "
	if (a==3) qstr+=" exactly ";
	else qstr+=" at least ";
	qstr+= a;
	if (a==1) qstr+=" head is obtained.";
	else qstr+=" heads are obtained.";
	hint+="There are 8 possible outcomes for this experiment:<br>";
	hint+="HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.";
}

function q11(){
	var a = rnd(2,6);
	var b = a-1;
	ans=b+"/6";
	qstr+="If a single six-sided die is rolled once, what is the probability of getting ";
	qstr+="<br>a score less than " + a + "?";
	qstr+="<br>Give your answer as a fraction.";
	hint+="There are " + b + " ways a die can give a score less than " + a + ".";
}

function q12(){
	var t, j;
	var a = new Array();
	a[1] = rnd(8,12);
	a[2] = a[1];
	a[3] = a[1];
	a[4] = a[1] + rndz(-3,3);
	a[5] = a[4];
	a[6] = a[1] + rndz(-1,1)*rnd(4,7);
	a[7] = a[1] + rndz(-1,1)*rnd(4,7);
	ans = a[1];
	for (var i=0; i<10; i++ ) {
		j = rnd(2,7);
		t = a[j]; a[j] = a[1]; a[1] = t;
	}
	qstr+="Find the mode of the numbers in the following sample:<br><br><center>";
	for (i=1; i<=7; i++) qstr+= a[i] + ", ";
	qstr+="</center>";
	hint+="The mode is the number which occurs most often in the sample.";
}

function q13() {

}

function q14() {

}

function q15(){

}

function q16(){

}

function q17() {

}

function q18() {	

}

function question(n) {
	do {
		choice=rnd(1,12);
	} while (choice==last1 || choice==last2 || choice==last3);
	last3=last2;
	last2=last1;
	last1=choice;
	qstr="";
	hint="";
	switch (choice) {
		case 1: q1(); break;
		case 2: q2(); break;
		case 3: q3(); break;
		case 4: q4(); break;
		case 5: q5(); break;
		case 6: q6(); break;
		case 7: q7(); break;
		case 8: q8(); break;
		case 9: q9(); break;
		case 10: q10(); break;
		case 11: q11(); break;
		case 12: q12(); break;
		case 13: q13(); break;
		case 14: q14(); break;
		case 15: q15(); break;
		case 16: q16(); break;
		case 17: q17(); break;
		case 18: q18(); break;
		default: alert("cannot happen! choice = " + choice);
	}
}