What's the day?

Probability Level 2

In a certain year there were exactly 4 Fridays and exactly 4 Mondays in January. On what day of the week did the 20th of January fall that year?

Saturday Wednesday Sunday Monday

Bold Drew by Bold Drew , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Dawar Husain
Dec 22, 2014

The only possible configuration is when the month starts on Tuesday.

If the month starts on either Wednesday, Thursday, or Friday , the month will have 5 Fridays . If the month starts on either Saturday, Sunday or Monday , the month will have 5 Mondays .

Now we can easily calculate the 20th January.

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Anna Anant
Dec 24, 2014

Let A,B,C, ..G be days of a week. If A is the first of january so A=1,8,15,22,29 and th 31th day is A+2 (C) we can say in january we have 5 times A, B and C. and 4times D,E,F and G. for satisfy the condition( the condition: in a certain year there were exactly 4 fridays and exactly 4 mondays in january ): D must be Friday and G monday. the 20th day is the 13th and 6th day = F F=G-1 = Monday-1=Sunday answer is Sunday

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Pradeep Ch
Dec 24, 2014

january has 31 days so each day appears four times till 28th .. as the next three consecutive days do not include monday and friday .... it is only possible when the three days are tuesday, wednesday, thursday .... so the 20th of january accordingly is sunday ....

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...