Blog Post #24: One True Treasure Beyond Measure

Dear Readers,

Even as a little boy around 50 years ago, I realised that time passes very quickly, and I talked with my mother about it then. Fast-forwarding half a century to now, Mum is no longer here as she was, but I do not have even the tiniest doubt that she and everyone who believes and recognises that part or whole centuries are nothing compared to what we can have later with God in Heaven if we love Him and each other, will freely receive that eternal gift, soon. So, instead of being distracted by any fleeting worldly things which will all vanish without importance, encourage people to focus on using their time and talents well to help each other in good ways that are pleasing to God. We cannot be perfect like God is, but if we are dedicating our lives to God, or will now start really doing so to honour and thank Him, then we can look forward to enjoying a perfect place with Him forever. Recognising that, helps us to focus not on transient pleasures; but on one true treasure beyond measure, promised through Jesus. For further reading, a wonderful, inspiring book which I warmly recommend is Sarah Young’s “Jesus Calling”.

Prayer is one’s personal communication with God, and really can be something to look forward to. In fact, nothing need stop us from offering up everything we do as a beautiful prayer.

I do like the following well-known prayer, as it’s a helpful reminder to begin each day well, right from the start.

I woke up early one morning

And rushed straight into the day

I had so much to accomplish

That I didn’t have time to pray

Problems just tumbled about me

And heavier became each task

“Why doesn’t God help me?” I wondered

He said, “You didn’t ask.”

I tried to come into God’s presence

I used all my keys in the lock

God gently and lovingly chided,

“My child, you didn’t knock.”

So, I woke up early this morning

And paused before entering the day

I had so much to accomplish

That I had to take time to pray.

The “Our Father” or “The Lord’s Prayer” is perfect in every way.

And here is another wonderful prayer/reflection for all times.

PAUL’S PAIRS PUZZLE

Paul thought of five different whole numbers. (In order from the smallest to the largest, let’s call the numbers a, b, c, d and e for now, until you discover them exactly…) Next, Paul calculated all the different “pair-wise sums” that result from adding any two of the different whole numbers together. The results were:

24, 26, 27, 28, 29, 30, 31, 32, 34, 35.

  1. How much more is ‘c’ than ‘b’? (Hint: Consider which of the bold numbers represent a+b and a+c.)
  2. How much more is ‘d’ than ‘c’? (Hint: Consider which of the bold numbers represent e+c and e+d.)
  3. How much more is ‘e’ than ‘a’? (Hint: Consider which of the bold numbers represent a+c and e+c.)
  4. How much more is d than b? (Hint: Use your answers to questions 1 and 2 above.)
  5. Which of the following must give odd number totals, and which must give even number totals: b+c; b+d; c+d; a+e?
  6. Which of the ten bold numbers must represent a+e? (Hints: Is a+e odd or even? Also consider which pairs must clearly be more than a+e, or less than a+e. Consider the same questions for b+c.)
  7. Now write down exactly what numbers a, b, c, d and e must be.

SECURE TIN PUZZLE

Rearrange the letters of SECURE TIN to make a proper 9-letter English word.

TIN JOKE!

What did the Tin Man say when got run over by a steamroller?

“Oh no! Foiled again!”

RANKS AS A CHESS BRAINTEASER!

Your fun chess brainteaser is to figure out just exactly where Black’s king should be placed on the missing 1st or 2nd rank so that White can then move and force checkmate in just two moves.

PUZZLE SOLUTIONS

PAUL’S PAIRS PUZZLE

24, 26, 27, 28, 29, 30, 31, 32, 34, 35.

24 26 27 28 29 30 31 32 34 35
a+b a+c e+c e+d
  1. How much more is ‘c’ than ‘b’? (Hint: Consider which of the bold numbers represent a+b and a+c.)

The two smallest pairs have to be a+b=24 and a+c=26. Comparing those two can show us that c must be 2 more than b, because 26 is 2 more than 24.

  1. How much more is ‘d’ than ‘c’? (Hint: Consider which of the bold numbers represent e+c and e+d.)

The two largest pairs have to be e+d=35 and e+c=34. Comparing those two can show us that d must be 1 more than c, because 35 is 1 more than 34.

  1. How much more is ‘e’ than ‘a’? (Hint: Consider which of the bold numbers represent a+c and e+c.)

Comparing a+c=26 and e+c=34 can show us that e must be 8 more than a, because 34 is 8 more than 26.

  1. How much more is d than b? (Hint: Use your answers to questions 1 and 2 above.)

Since d is 1 more than c (see question 2) and c is 2 more than b (see question 1), it follows that d must be 3 more than b.

  1. Which of the following must give odd number totals, and which must give even number totals: b+c; b+d; c+d; a+e?

Whole numbers with an odd difference also have an odd sum. So, b+d and c+d must be odd. Whole numbers with an even difference also have an even sum. So, b+c and a+e must be even.

  1. Which of the ten bold numbers must represent a+e? (Hints: Is a+e odd or even? Also consider which pairs must clearly be more than a+e, or less than a+e. Consider the same questions for b+c.)

The available “slots” in the table now have to be filled as follows, including a+e=30 (smaller than e+b). Also, b+c=28 has to be smaller than b+d and c+d, and they have to be the odd numbers 29 and 31. That leaves only a+d, which has to be 27, the only remaining number yet to be taken.

24 26 27 28 29 30 31 32 34 35
a+b a+c a+d b+c b+d a+e c+d e+b e+c e+d
  1. Now write down exactly what numbers a, b, c, d and e must be.

Already knowing b+c=28 and c is 2 more than b gives: b=13 & c=15. That allows us to work through the above table to get: a=11, d=16 & e=19.

Summary: a=11, b=13, c=15, d=16 & e=19.

SECURE TIN PUZZLE

SECURE TIN rearranges to give CENTURIES.

RANKS AS A CHESS BRAINTEASER!

If we place Black’s king on h1, then White forces checkmate with 1 Qf2! h2 2 Qf1#.

As it’s now less than 6 weeks until Christmas, I’ll finish with this powerful yet peaceful picture & link:

https://www.youtube.com/watch?v=sR8rlTIU8_Y Please enjoy a beautiful song via the link, 6mins 50secs.

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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