100 using Digits from 1 to 9

Classic Problem

Using just the digits $1$ to $9$ in order (ascending and descending), using the usual operations ($+$, $-$, $\times$, $\div$) and brackets, how can you make $100$?

Solution

There are many answers:

$1 + 2 + 3 + 4 + 5 + 6 + 7 + \paren {8 \times 9} = 100$

$123 - 45 - 67 + 89 = 100$

Using the digits in reverse order:

$98 - 76 + 54 + 3 + 21 = 100$

... and of course the initial answer:

$\paren {9 \times 8} + 7 + 6 + 5 + 4 + 3 + 2 + 1$

$\blacksquare$

Historical Note

This puzzle was posed, and solutions provided, by Henry Ernest Dudeney.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $100$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $100$