Blog Post #64: For Haley, Myriam, My Little Sister, Peter The Great AND a school pussy cat!

Dear Readers,

Happy Haley, a talented student at my school, recently surprised me with a lovely painting that she made as a New Year’s gift.

Haley enjoys solving puzzles, and so I’m featuring her in the following one together with Peter and Myriam, two adult friends of mine. Peter and Myriam have exactly the same birthday as each other (regarding the day, month and year), and in this puzzle let’s assume that their ages are currently whole numbers.

THE PETER-MYRIAM-HALEY BRAINTEASER

If P and M are the current ages of Peter and Myriam, and H is Haley’s favourite whole number, what is the last digit on the right of (P+M) to the power of (4xH) ? I had to include the number 4, otherwise the pussy cat might feel left out!!

Pictured below: Peter The Great with a happy cat!

BONUS PUZZLE FOR MY LITTLE SISTER!

My youngest sister will turn 7×7 in 3×3 days from now. If we write dates in the six-digit form DDMMYY, then all dates this month will have the form DD0120. Only one of them is an exact multiple of 49, and that’s 190120 today! There are only two FIVE-DIGIT whole numbers ending in 120 which are exact multiples of 49. Can you find them without using a calculator?

A CUTE CHECKMATE CHALLENGE!

Part 1: Imagine that White has one extra, invisible pawn somewhere on the board. That pawn must remain in the same place in Part 2 of the puzzle. Where exactly is the invisible pawn if (immediately after placing it on the board) White can deliver checkmate right away in one move?

Part 2: Suppose instead that White has the same invisible pawn in the same place as in part 1, but one of White’s other pawns vanishes, and so does one of Black’s pawns! Exactly which pawns vanish, if it is now Black to move and force checkmate in at most 5 moves?

Solutions to the puzzles will be published at the time of the next blog post, and in the meantime I wish you lots of happiness…and great fun with the puzzles!

With very best wishes as always,

Paul Motwani xxx

Author: Paul A. Motwani

My name is Paul Motwani, but my colleagues, my students and their parents mostly call me "Mr. Mo"! My middle initial, A, stands for Anthony, because I was born on the official feast day of St. Anthony of Padua, the patron saint of miracles and of lost souls. I love teaching Mathematics and Chess, and giving fun-packed talks and shows in schools and clubs. The popular ingredients of Math, Chess, Mystery and Magic are my "Fantastic Four", and I give prizes too! I am an International Chess Grandmaster, and (loooooong ago!) I was the World Under-17 Champion. I am the author of five published chess books and hundreds of newspaper articles. I live with my wonderful wife and son in Belgium. I also love music, movies and puzzles. I blog at paulmotwani.com. My e-mail address is pmotwani141@gmail.com. You can find me on Facebook, too.

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