Blog Post #49: Seventy Times Seven

Dear Readers,

Happy St. Andrew’s Day! Yes, November 30th is the official Feast Day of St. Andrew, the patron saint of my original home country of Scotland. In this Blog Post #7 x 7 today, I am reminded of the importance of people forgiving each other seventy times seven times or as often as needed, just as Jesus said and continues to do for us all. When you and I also remember and practise that way with everyone, it leads to more peace and happiness.

I wish you a wonderful weekend now. In case you enjoy dabbling in Math puzzles, here comes a couple of wee personal ones from me that you might like to try.

THE 49 PUZZLE

Suppose that a student scores 49 points in a test. If the test is out of a total of 50 points, then 49/50 is equivalent to a 98% result. Your challenge is to find all the different possible whole number test totals such that a score of 49 points in the test would be equivalent to a whole number percentage (with no decimals needed). For example, 49/49 is equivalent to a perfect, maximum 100% result. In addition to already noting that the test total could have been 50 points or 49 points, can you now find fourteen other possible test totals?

A solution is posted further down.

 

THE 49 SQUARED PUZZLE

The square of 49 is 49 x 49=2401, which is precisely 1 more than a whole multiple of a hundred since 2401=2400+1.

Can you find the next three cases of whole numbers whose squares are precisely 1 more than a whole multiple of a hundred?

A solution is posted further down.

SOLUTIONS TO PUZZLES

SCORE TEST TOTAL PERCENTAGE
49 4900 1
49 2450 2
49 1225 4
49 980 5
49 700 7
49 490 10
49 350 14
49 245 20
49 196 25
49 175 28
49 140 35
49 100 49
49 98 50
49 70 70
49 50 98
49 49 100

 

51 squared=2601; 99 squared=9801; 101 squared=10201

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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