Another Weird Test Question

I found this puzzle on Facebook:

Puzzle. Solve this:
1+4 = 5,
2+5 = 12,
3+6 = 21,
5+8 = ?
97% will fail this test.

Staring at this I decided on my answer. Then I looked at the comments: they were divided between 34 and 45 and didn’t contain the answer that initially came to my mind. The question to my readers is to explain the answers in the comments and suggest other ones. Can you guess what my answer was?


Day and Night

Puzzle. The length of the day today in Boston is the same as the length of the coming night tonight. What is the total length of both?


How Old is Everyone?



Bob: My older brother is 30 years older than me.
Carl: My mom is 8 times older than me.

How old is everyone?


Cube Sudo-Kurve

Last year, when I read an application file of Wayne Zhao to PRIMES, I got very excited because he liked puzzles. And I’ve always wanted to have a project about puzzles. After Wayne was accepted to PRIMES we started working together. Wayne chose to focus on a variation of Sudoku called Sudo-Kurve.

We chose a particular shape of Sudo-Kurve for this project, which ended up being very rewarding. It is called Cube Sudo-Kurve. The Cube Sudo-Kurve consists of three square blocks. The gray bent lines indicate how rows and columns continue. For example, the first row of the top left block becomes the last column of the middle block and continues to the first row of the bottom right block. As usual each row, column, and square region has to have 9 distinct digits.

Cube Sudo-Kurve

Wayne and I wrote a paper Mathematics of a Sudo-Kurve, which has been published at Recreational Mathematics Magazine.

A Cube Sudo-Kurve needs at least 8 clues to have a unique solution. Here we have a puzzle with 8 clues that we designed for our paper.


Emissary Puzzles

I’ve been invited to help with the Puzzle Column at the MSRI newsletter Emissary. We prepared six puzzles for the Fall 2018 issue.

I love the puzzles there. Number 2 is a mafia puzzle that I suggested. Number 6 is a fun variation on the hat puzzle I wrote a lot about. Here is puzzle Number 3.

Puzzle. Let A = {1,2,3,4,5} and let P be the set of all nonempty subsets of A. A function f from P to A is a “selector” function if f(B) is in B, and f(B union C) is either equal to f(B) or f(C). How many selector functions are there?


Cave Lioness

(Photo by Rebecca Frankel.)

Cave Lion





My Phone

Once I was giving a math lecture and my phone, which I’ve never quite understood, was on the desk in front of me. Suddenly it rang. I didn’t pick it up, as I proceeded with my lecture. The ringing stopped, while I was explaining a particularly interesting mathematical point. After a minute, my phone said, “I do not understand a word you are saying.”


The Halfsies

Detective Radstein is investigating a robbery. He apprehends three suspects: Anne, Bill, and Caroline. The detective knows that no one else could have participated in the robbery. During the interrogation the suspects make the following statements:

  • Anne: I didn’t do it. Bill did it alone.
  • Bill: I didn’t do it. Caroline did it.
  • Caroline: I didn’t do it. Bill did it.

Detective Radstein also discovered that all three suspects are members of a club called The Halfsies. Every time they speak, they make two statements, one of which is a lie and the other one is true. Who committed the robbery?


Less Annoying Hyperbolic Surfaces

Less Annoying Hyperbolic Surfaces

I already wrote about my first experience crocheting hyperbolic surfaces. In my first surface I added two more stitches per current stitch. It took me hours to crochet the last row: the same hours it took me to crochet the rest.

For my next project, I reduced the ratio. The light blue thingy has ratio 3/2. I continued making my life simpler. The next project, the purple surface on the left, has ratio 4/3. The last project on the right has a ratio of 5/4 and is my favorite. Mostly because I am lazy and it was the fastest to make.


Fast Thinking

How much time will it take you to answer the following question?

Can the equation 29x + 30y + 31z = 366 be solved in natural numbers?