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
Paul Motwani 