Q:

Iterate through an array, testing that EVERY element is larger than a certain number

I've got a really clunky way to do it.  But wanted to figure out a leaner looped method.  I want to go through my array, and test every element is above a certain value.  in this case say, 50. 
Heres what I've got:
boolean found0 = false;
for (int k = 0; k < array.length ; k++) {
  if (array[0] >= 50 &&
      array[1] >= 50 &&
      array[2] >= 50 &&
      array[3] >= 50 &&
      array[4] >= 50 &&
      array[5] >= 50) {
    found0 = true;
  }
}

A:

Since your iterating variable is called k, you can check the kth element in the array for >= 50.  
If some of the array elements is less than 50, we can set the flag to false and break the loop. 
boolean ok = false;
for (int k = 0; k < array.length ; k++) {
    if (array[k] >= 50) {
        ok = true;     
    } else {
        ok = false;
        break; //Break the loop, because we have at least one, which is < 50
    }
}

Even better, we can get shorten the if/else statement and check if we have at least one element, less than 50. 
boolean ok = true;
for (int k = 0; k < array.length; k++) {
   if (array[i] < 50) {
       ok = false;
       break;
   }
} 

