Know Without Trying: Maximum and Minimum Problems

Methods in this video

Tap a time to jump to where the video teaches that method.

1. 1

   Biggest digit in the highest place

   ▶ 0:50

   When to use it: Using some number cards or different digits to make the largest or smallest number (or the sum or difference of such numbers), or to make something that is compared by size or order (the latest date in the year); the question says the largest, the smallest or the latest.

   • Largest: start at the highest place and put the biggest digit left in each place.
   • Smallest: use the smallest digits, but 0 can't go first; put 0 second.
   • The highest place isn't always first: whatever the question compares first is the highest place (for dates, the month before the day).
2. 2

   Make every piece as big as it can be

   ▶ 4:47

   When to use it: The question asks for the fewest pieces (the fewest coins, the fewest turns) or, with limited money, the most you can buy; the pieces come in different sizes, or each step has a limit (each turn is an acute angle, less than 90°). The question says as few … as possible, the smallest number of times, or the most.

   • Fewest pieces: make each one as big as possible; start with the biggest.
   • If the leftover can't be swapped, count it too.
   • If each piece can't quite reach the limit, push it as far as it goes; if it's still a little short, add one more.