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Can You Figure out When Denise’s Birthday Is?

June 24, 2016 | Joanne Kennell

Denise's birthday puzzle

You are going to need a pencil and eraser to solve this puzzle. Make sure you try it on your own first!

Let’s get started. We know that Albert knows the month of Denise’s birthday, while Bernard knows the date, and Cheryl knows the year. What you have to pay attention to is what each person is saying.

First, Albert says, “I don’t know her birthday, but I know Bernard doesn’t know.” Of course Albert can’t know because every month appears more than once, but how can he know that Bernard doesn’t know? You need to count the number of times a date appears.

When you count them up, you will notice that the dates 11 and 12 occur only once. What this means is that we can remove any dates with 11 and 12: June 12 and April 11. Otherwise, Bernard would know Denise’s birthday. But since Albert knows the month, this also means that the date isn’t in June or April, so we can also get rid of all dates with June and April.

SEE ALSO: Can You Figure out How to Divide This Shape?

What we are left with is:

2001 — Feb. 17, Mar. 13, May 15
2002 — Mar. 16, May 14, Aug. 16
2003 — Jan. 13, Feb. 16, Mar. 14, Jul. 16

2004 — Jan. 19, Feb. 18, May 19, Aug. 18

Next, Bernard says, “I don’t know her birthday, but I know Cheryl doesn’t know.” Both the first and second part of his sentence gives us information. The only way Bernard could know Denise’s birthday is if he has a date that occurs only once, so we can remove all dates that happen just once: 17, and 15. Leaving us with:

2001 — Mar. 13
2002 — Mar. 16, May 14, Aug. 16
2003 — Jan. 13, Feb. 16, Mar. 14, Jul. 16

2004 — Jan. 19, Feb. 18, May 19, Aug. 18

But Bernard also says he knows Cheryl doesn’t know, but that could only be true if there is a year with only one date: 2001. But since the date under the year 2001 is May 13, and Bernard knows the date, Denise’s birthday must not be the 13th, so we can also get rid of any date with 13.

What we are left with is:

2002 — Mar. 16, May 14, Aug. 16
2003 — Feb. 16, Mar. 14, Jul. 16

2004 — Jan. 19, Feb. 18, May 19, Aug. 18

We are getting closer!

Now, Cheryl says, “I don’t know her birthday, but I know Albert doesn’t know.” If Cheryl knows that Albert doesn’t know, that means we can eliminate any year where there is a month that occurs only once in the entire spread. January occurs only once, so we can get rid of the year 2004. We are left with:

2002 — 16 Mar, 14 May, 16 Aug

2003 — 16 Feb, 14 Mar, 16 Jul

Albert exclaims, “Now I know her birthday,” but how can he know? If Albert knows, there can only be one occurrence of that month, so we can get rid of March, which occurs twice. We have:

2002 —14 May, 16 Aug

2003 — 16 Feb, 16 July

Next, Bernard shouts, “I know too.” For this to be true — since Bernard knows the date — it must be a day that appears only once. Luckily for us, the number 16 shows up three times.

What are we left with? May 14.

Were you able to solve it on your own?

Try another brain teaser: There’s More to This Riddle Than Might First Appear

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