Blog Post #53: Incredible!

Dear Readers,

Since last August, I have been very happy and grateful for getting to work on Mathematics with wonderful students in a beautiful new school. Isabelle is one who loves to sketch creative drawings when she finishes Maths tests early with some minutes to spare. Today, I will feature a brainteaser about the following picture.

BRAINTEASER INSPIRED BY ISABELLE’S DRAWING

Isabelle used a free page from her school diary, but the drawing was actually made exactly 2n weeks after the date shown on the page, where the exponent n is the largest whole number that is possible to-date.

Your fun challenge is to figure out the value of n, and the precise date on which Isabelle actually drew her drawing.

A solution will be posted in April.

In the meantime, I wish everyone a wonderful weekend now, bringing happiness to others too.

Solution to brainteaser in Blog Post #52

The challenge was to find the maximum number of consecutive positive whole numbers which, when all added together, produce a total sum of exactly 15219.

OK, a standard formula for the sum of the first n natural numbers is S=n(n+1)/2, and so 2S=n(n+1). Therefore, n will be slightly less than the square root of 2S. Now, √(2×15219) is roughly 174.5, which suggests trying 174 for n. In that case, n(n+1)/2=174×175/2=15225, which only very slightly overshoots 15219 by six. Since 1+2+3=6, our sum 1+2+3+…+172+173+174 will be exactly right if we trim it to 4+5+6+…+172+173+174=15219. That is the optimal sum of 171 consecutive positive whole numbers for getting a total of 15219.

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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