1991 AMC 8 Problem 1

Question

What is the value of

\begin{aligned} &1{,}000{,}000{,}000{,}000 \\ &\quad {}- 777{,}777{,}777{,}777? \end{aligned}

222{,}222{,}222{,}222

222{,}222{,}222{,}223

233{,}333{,}333{,}333

322{,}222{,}222{,}223

333{,}333{,}333{,}333

Think of the amount you must add to

777{,}777{,}777{,}777

to reach

1{,}000{,}000{,}000{,}000

Work from the right: the units digits must add to

10

with a carry, and every other column then adds to

10

with that carry

Lining up the subtraction gives

\begin{aligned} &1{,}000{,}000{,}000{,}000 \\ &\quad {}- 777{,}777{,}777{,}777 \\ &= 222{,}222{,}222{,}223. \end{aligned}

Equivalently, to climb from

777{,}777{,}777{,}777

up to

1{,}000{,}000{,}000{,}000

you add

3

in the units place and

2

in each of the other eleven places.

Thus, the correct answer is B .

Problem 1 in other years