2006 AMC 10B Problem 16

Question

Leap Day, February

29,

2004,

occurred on a Sunday. On what day of the week will Leap Day, February

29,

2020,

occur?

Tuesday

Wednesday

Thursday

Friday

Saturday

Count the days from one Leap Day to the next:

3\cdot365+366

That total is

1461\equiv 5\pmod 7,

so each

4

-year cycle advances the weekday by

5

From one Leap Day to the next is

3\cdot365+366=1461

days, and

1461\equiv 5\pmod 7.

Over the four cycles from

2004

to

2020,

the weekday advances

4\cdot5=20\equiv 6\pmod 7,

that is,

6

days forward, which is one day back from Sunday.

So Leap Day

2020

falls on a Saturday.

Thus, the correct answer is E.

Problem 16 in other years