Blog Post #36: With Love and Thanks to Alex and Karen

Dear Readers,

My wife, Jenny, and I returned home last night from a wonderful 3-day business/leisure trip to Berlin with Jenny’s boss, Alex, and his wife, Karen, who is a former colleague of mine. Outside Alex and Jenny’s working hours, we could all enjoy seeing Germany’s beautiful capital city.

You could trust me to also notice numbers everywhere, but Karen mentioned bigger ones, as she saw from the pedometer app on her phone that we all took many thousands of memorable footsteps in Berlin!

BRAINTEASER FROM BERLIN!

As three is my favourite number, can you find two numbers with a difference of 3 and a quotient (dividing one number by the other) of 0.925? Algebra and/or calculators may be used, but neither of them are actually needed.

BRAINTEASER STARRING JENNY & KAREN!

Another of my favourite numbers is 13, because June 13 is my birthday. Jenny and Karen also like their own birthday day numbers. If I tell you that the product of Jenny’s and Karen’s numbers (multiplied together) is 384, then your fun brainteaser is to now figure out Jenny’s number and Karen’s number–which is actually the bigger of the two.

BRAINTEASER STARRING ALEX & KAREN!

If you’ve already solved Jenny & Karen’s brainteaser, then you’re perfectly placed to now solve Alex & Karen’s brainteaser! The product of Karen’s birthday day number (multiplied) together with Alex’s birthday day number equals an exact whole multiple of 100. Your fun brainteaser is to figure out Alex’s birthday day number.

I hope that you have got lots of enjoyment out of reading this post, and trying some or all of the fun puzzles. Jenny and I wish you a lovely weekend now, and a very happy Chinese New Year if you celebrate that, too.

Don’t worry; we (seriously now) wouldn’t dream of eating all of that yummy Chinese food ourselves!!

SOLUTIONS TO PUZZLES

BRAINTEASER FROM BERLIN!

As three is my favourite number, can you find two numbers with a difference of 3 and a quotient (dividing one number by the other) of 0.925? Algebra and/or calculators may be used, but neither of them are actually needed.

SOLUTION

0.925=925/1000. There are four 25s in every 100, and forty 25s in 1000, while 925 is 75–or three 25s–less, and so is equivalent to thirty-seven 25s. Therefore, an equivalent fraction for 925/1000 is 37/40, while another sneaky one is -37/-40.

So, 37 divided by 40 equals 0.925, as does negative 37 divided by negative 40.

BRAINTEASER STARRING JENNY & KAREN!

Another of my favourite numbers is 13, because June 13 is my birthday. Jenny and Karen also like their own birthday day numbers. If I tell you that the product of Jenny’s and Karen’s numbers (multiplied together) is 384, then your fun brainteaser is to now figure out Jenny’s number and Karen’s number–which is actually the bigger of the two.

SOLUTION

384 can easily be “split” into small factors by repeatedly dividing it by 2. Doing so, leads to 384=2x2x2x2x2x2x2x3. Those factors have to be shared out between Jenny’s birthday day number and Karen’s birthday day number–neither of which can possibly exceed 31, the maximum number of days in any month. So, 2x2x2x2x2=32 would already be too big.

Therefore, the only possibility is 2x2x2x2=16 for Jenny, and 2x2x2x3=24 for Karen, as we were given that Karen’s number is the bigger of the two.

BRAINTEASER STARRING ALEX & KAREN!

If you’ve already solved Jenny & Karen’s brainteaser, then you’re perfectly placed to now solve Alex & Karen’s brainteaser! The product of Karen’s birthday day number (multiplied) together with Alex’s birthday day number equals an exact whole multiple of 100. Your fun brainteaser is to figure out Alex’s birthday day number.

SOLUTION

As 24x25=600–an exact whole multiple of 100–and no other suitable smaller or bigger birthday day numbers are available to give such a result, we can deduce that Alex’s birthday is on the 25th (and it’s actually this month!). So, Jenny and I would like to wish Alex a very happy birthday, coming up in only 3×3 days’ time!

In Berlin, I learned that Karen’s dad is a retired church minister whose 75th birthday is coming up on March 28, next month. In the Holy Bible, the number 40 features very often in special ways. As it’s now exactly forty days until March 28, I would like to include special, early, happy birthday wishes here for Karen’s dad xxx

Even the sweetness of the giant chocolate tower below does not adequately quantify the sweet birthday wishes! 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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