Once I visited her family for dinner and asked her point blank, “How old are you?” Here is the rest of the conversation:

Alice: I am two times older than my younger son was 5 years ago.

Bob: My mom is 12 times older than my older brother.

Carl: My younger brother always multiplies every number he mentions by 24.

Bob: My older brother is 30 years older than me.

Carl: My mom is 8 times older than me.

Alice: My older son always multiplies every number he mentions by 2.

How old is everyone?

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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.

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.

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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.

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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?

When I was in grade school, one of the teachers called me Cave Lioness. She hated my unruly hair, which reminded her of a lion’s mane. This teacher was obviously very uninformed, for female lions do not have manes.

This name calling had the opposite to the desired effect. I became proud of my mane and didn’t ever want to cut it. When I grew older, I opted for convenience and started to cut my hair short&mdahs;sometimes very short.

Last year I was too busy for barbers, and my hair grew more than I intended. As it turned into a mane, I remembered the story of this nickname.

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- 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?

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.

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Share:]]>Can the equation 29

x+ 30y+ 31z= 366 be solved in natural numbers?

Happy 2019, the first 4 digit number to appear 6 times in the decimal expansion of Pi.

By the way:

2019 = 1^{4} + 2^{4} + 3^{4} + 5^{4} + 6^{4}.

Also, 2019 is the product of two primes 3 and 673. The sum of these two prime factors is a square.

This is not all that is interesting about factors of 2019. Every concatenation of these two prime factors is prime. Even more unusual, 2019 is the largest known composite number such that every concatenation of its prime factors is prime. [Oops, the last statement is wrong, Jan 3,2019]

Happy Happy-go-Lucky year, as 2019 is a Happy-go-Lucky number: the number that is both Happy and Lucky.

In case you are wondering, here is the definition of Happy numbers: One can take the sum of the squares of the digits of a number. Those numbers are Happy for which iterating this operation eventually leads to 1.

In case you are wondering, to build the Lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, …. The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, …. The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, …. The next number remaining is 9, so delete every ninth number, etc.

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