Blog Post #30: 110% NOT BY CHANCE

Dear Readers,

If you are visiting this site today in the hope of finding some interesting, fun, thought-provoking Math, Chess and word puzzles, then you will certainly not be disappointed, for they are all here in abundance…together with a happy message of far greater importance, which I hope you will choose to share with as many other people as possible, for their benefit. For me, personally, the happy message is the very best part, and it will definitely be given just a little bit later on.

MIGHTY LITTLE WORD PUZZLE!

Change just one letter of the word MIGHTY to make a number…

I’m going to congratulate you right now, because I have no doubt that you’re already thinking about EIGHTY.

Regarding today’s blog post title, I cannot help thinking about the number 80, the “extra” in 110 compared with 30. I promise we’ll “correct” that shortly by subtracting 80 during the following fun numbers game intended to wish you well.

WISHING WELL

Step 1: You can choose almost any three-digit number you like, but just make sure that the positive difference between the first and last digits is not less than two (e.g. 301 or 103 are OK here, but 302 or 203 are not)

Step 2: Reverse the three-digit number you chose in step 1 (e.g. if you chose 301, you’ll reverse it to get 103)

Step 3: Looking at your numbers in step 1 and step 2, subtract the smaller number from the bigger number

Step 4: Now reverse the answer you got in step 3

Step 5: Add together the numbers you got in step 3 and step 4

Step 6: As promised before, subtract 80

Step 7: As this is meant for you and your friends, double the answer you got in step 6.

You’ll see from your final result that I mean to wish you a magical, happy time in 2018 !!

HELP EVERYONE TO C IT!

Can you think of a proper, three-letter, English noun which can be made plural by inserting a letter c before the end instead of adding an s to the end?

A photo is included as a big clue !!

If you’re having thoughts like, “I’ll die if I don’t see it!” then congratulations: the plural of die (when used as a noun instead of a verb) is dice !

By the way, even though we can’t see them in the photo, which numbers must be on the back face and the bottom face of the pictured die? The answers are two and four, because “front+back” and also “top+bottom” always equals seven, as surely as “God+Love” guarantees you Heaven forever on the other side of this life.

Of course, the real proof of that is to be found not in any mathematical or scientific explorations, but rather in God’s perfect love, gift and sacrifice of Jesus for us. We only need to humbly and gratefully accept the gift, by loving God and each other as Jesus taught, and we are assured of a glorious place in Heaven forever, after our short lives on Earth now. “The world and its desires pass away, but whoever does the will of God lives forever”–John 2:17 in The Bible, New International Version.

A PROPOSAL

Right now, I have an interesting proposal for you… Imagine that you are looking at a die, face-on, as in the second-last photo (given before).

Option 1: You can roll the die once; note the number on the front and multiply it by the sum total of the other five numbers (e.g. 5 x (1+2+3+4+6)=5 x 16=80)

OR

Option 2: You can roll the die once; note the numbers on the front and the top, and multiply their sum total by the total of the other four numbers (e.g. (5+3) x (1+2+4+6)=8×13=104).

In either case, you need a score of 50 or more to pass. Scores of 100 or more are outstanding. Which option would you choose? Which number would you like to “wish” or “ask” for on the front of the die?

Personally, I definitely choose Option 2. To me, the number we might get on the front is a bit like us, if thinking alone and randomly, but in combination with the number above it’s something really special from God. By accepting His gift, it’s not possible to fail in the end. In fact, if we ask in faith for the maximum in order to put it to good use, then we can expect outstanding results, sooner or later.

(Just for the record, Option 2 guarantees at least (1+2) x (3+4+5+6)=3×18=54. With a maximum 6 on the front (which means 1 is on the back face), the number on top is guaranteed to be 2 or more, up to 5, and the total score is guaranteed to be over 100: (6+2) x (1+3+4+5)=8×13=104 or (6+3) x (1+2+4+5)=9×12=108 or (6+4) x (1+2+3+5)=10×11=110 or (6+5) x (1+2+3+4)=11×10=110 again!)

The real moral of the story of this: please continue, or begin now, living your life with love for God and for each other. I promise to do that, too, and we will have a happy, never-ending, true story! Thank you for please passing on the Good News message to others. “O God, from my youth You have taught me, and I still proclaim Your wondrous deeds”–Psalm 71:17.

CHECKMATE IN A MERE 3 MOVES!!

In this delightful chess composition by Dr. Fritz Emil Giegold (1903-1978), it’s White to play and force checkmate in a mere 3 moves!!

A THREE WISHES JOKE (TOLD TO ME BY A FUNNY FRIEND)!

A brunette, a redhead and a blonde are stranded on an island. One day, the three of them are walking along the beach and they discover a magic lamp. They rub and rub, and sure enough, out pops a genie. The genie says, “Since I can only grant three wishes, you may each have one.”

The brunette says, “I’ve been stuck here for years. I miss my family, my husband, and my life. I just want to go home.” POOF! The brunette gets her wish and she is returned to her family.

Then, the redhead says, “I’ve been stuck here for years as well. I miss my family, my husband, and my life. I wish I could go home too.” POOF! The redhead gets her wish and she is returned to her family.

The blonde starts wailing uncontrollably. The genie asks, “My dear, what’s the matter?” The sobbing blonde answers, “I wish my friends were still here.”

P.S. “Going blonde is like buying yourself a light bulb!” is a witty quote from a world-famous celebrity model, television personality, businesswoman, fashion designer, singer, television producer, author, and actress.

SOLUTIONS TO PUZZLES IN BLOG POSTS #28 & #30

THE 28-PUZZLE

I’m thinking of a particular three-digit whole number in which all the digits are equal. Let’s represent the number by LLL. Your fun challenge is to find the number, given that LLL+LLL+Lx28=1000. (Everything is of course in base ten, as normal!)

ANSWER: LLL=444.

LOOK AT THE ROOKS!

  1. Why is 1 Kc3?? a losing blunder?
  2. A type of “Helpmate” in 2 moves! Can you find an even worse path in which White chooses a different starting move in the position above, and, after a particular reply from Black, White deliberately plays the worst possible move which then allows Black to deliver checkmate right away!?

ANSWERS: 1 Kc3?? loses to 1…Nd5+ 2 Kc4 Nb6+ or 2…Rc2+ 3 Kb5 Nc7+.

1 Ka1 Nd3 2 Ra2?? allows 2…Re1# while 1 Kb1 Nd3 2 Ra1?? allows 2…Rb2# !

CELEBRATING WITH EVELYN & MISCHA

Evelyn and Mischa–two dear friends who really put 110% into all the good that they do–recently celebrated a total of 110 years between them. The following super-fun brainteasers were sent by e-mail to invited guests, in advance of Evelyn & Mischa’s special party.

CHRISTMAS BRAINTEASERS!

  1. What is special about the words

EVELYN AND MISCHA’S FEAST

FAST SMILES CANDY HEAVEN!?

ANSWER: EVELYN AND MISCHA’S FEAST contains exactly the same 21 letters as are used in FAST SMILES CANDY HEAVEN.

  1. Can you find a ten-digit positive whole number, with all its digits different, such that the number is a whole multiple of 110?

Keep to base ten!!

ANSWER: For a number to be a multiple of 110, it must be a multiple of 10 (which therefore ends with a 0 on the right) AND must also be a multiple of 11.

For the moment, if we think just about multiples of 11 such as 132 or 209 or 8371209, it’s helpful to note that 1+2=3 with the digits of 132; 2+9=0+11 regarding 209; 8+7+2+9=3+1+0+22 regarding 8371209.

Those examples illustrate an important property of all multiples of 11: the two sums of alternating digits must either be exactly equal (e.g. 1+2=3 with the digits of 132) or they must differ by a proper multiple of 11 (e.g. 2+9=0+11 regarding 209; 8+7+2+9=3+1+0+22 regarding 8371209).

Now, we’ve basically been asked to find a ten-digit whole number that ends with 0 on the right and also includes 1, 2, 3, 4, 5, 6, 7, 8 and 9 once each in some order, so that its ten digits will all be different.

The total sum of the ten digits will definitely be 0+1+2+3+4+5+6+7+8+9, which makes 45. Note that we can’t split that exactly equally into two sums of alternating digits, because half of 45 is 22.5 and that’s not a whole number.

However, we can arrange for one sum of alternating digits to be 11 more than the second sum of alternating digits. The bigger sum must be 28 and the smaller sum must be 17. The grand total will of course be 45.

A suitable number is 9543682170, for example, because 9+4+6+2+7=28 and 5+3+8+1+0=17. 28 is 11 more than 17. 9543682170÷110=86760747, a whole number, and so that works just fine.

(Note: It’s simply not possible, with the digits we have, to make one alternating sum of five digits 22 or 33 or 44 more than the second alternating sum of five digits. For instance, though a sum of 39 is 33 more than a sum of 6, and 39+6 gives a correct grand total of 45, how would we actually make the sums of 39 and 6, each using five different numbers from 0 to 9? It simply can’t be done! So, we have to settle for a difference of 11 between the two alternating sums.)

  1. In puzzle 2, can you find the biggest possible number that works?

ANSWER: The optimal biggest solution that fits all the previously discussed requirements is 9876524130.

After “slotting in” the optimal biggest digits 98765 to start with, and of course 0 at the very end to finish, it doesn’t take much longer to figure out that 2413 is the best we can do with the remaining four digits. 9+7+5+4+3=28 and 8+6+2+1+0=17, as is strictly required; otherwise our ten-digit number simply won’t work. 9876524130÷110=89786583.

  1. In puzzle 2, can you find the smallest possible number that works?

ANSWER: The optimal smallest solution that fits all the previously discussed requirements is 1234758690.

After “slotting in” the optimal smallest digits 1234 to start with, and of course 0 at the very end to finish, it doesn’t take much longer to figure out that 75869 is the best we can do with the remaining five digits. 1+3+7+8+9=28 and 2+4+5+6=17, as is strictly required; otherwise our ten-digit number simply won’t work. 1234758690÷110=11225079.

CHECKMATE IN A MERE 3 MOVES!!

White forces checkmate with 1 Nf6+ Kg7 2 Bc5!! (2 Bb4 or 2 Ba3 are equally effective, too) 2…Kxf6 3 Bd4#.

To finish, please enjoy a short but very beautiful piece of film music via the link below.

https://www.youtube.com/watch?v=i8fyP35T0HY

Define Love, 1 min. 35 sec., from a classic 1984 movie, Starman.

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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