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The student builds the greatest and smallest numeral from a set of digits and names the numeral just before or after a given one.
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Where each digit goes when you want the greatest or the smallest numeral.
To form the greatest numeral from a given set of digits, remember that the leftmost place holds the highest value. Place your largest digit there, and continue arranging the remaining digits in falling (descending) order.
Brain Teasers question 10, worked both ways.
Problem. Form the greatest and the smallest 5-digit numeral from the digits , using each digit exactly once.
Brain Teasers question 1(a), with the book's own four options.
What is the greatest 6-digit numeral formed by using the digits and exactly once?
Brain Teasers question 10, both parts.
Using the digits exactly once, write down the greatest and the smallest 5-digit numeral. Then, clearly explain what rule you applied for the digit .
Write both the greatest and smallest numerals separated by a comma.
Explain your handling of the digit 0 when forming the smallest numeral.
Optional: Where in daily life might you need to arrange numbers by size?
Adding one and taking one away, and what happens at a boundary.
To find the numeral just after a number, you simply add . To find the numeral just before a number, you take away.
Two Brain Teasers items on either side of a boundary.
When we want to find the numeral just before a given number, we subtract one. For example, the numeral just before is . This happens because subtracting one changes multiple place values at once, rolling the zeros backward into nines. On the other hand, finding the numeral just after means we add one. The greatest -digit numeral is . The numeral which is one more than the greatest -digit numeral is . This jump takes us from a -digit number straight into the smallest -digit number.