Ken's blog

One early and sunny Sunday afternoon at the Royal Banana Plantation Bridge Club, there arose an animated discussion as to whether hand A consisting of five clubs, four hearts, three diamonds and one spade was more probable than hand B with four spades, four hearts, four diamonds and one club.

Murphy Smythe thought that hand A would be more probable since there were more clubs. Sally Witheroak said that hand B was more certain as there were many fours and only one club.

The members of the Royal Banana Plantation Bridge Club took sides and split up into two contentious groups, each respectively supporting Smythe’s or Witheroak’s view. This led to multiple impassioned speeches that stretched into the early evening.

The argument was finally settled by Lenny, Sally Witheroak’s little son – who had a scientific calculator in his backpack – after Lenny arrived with his father to fetch mother home to make supper.

What would you say was more probable, hand A or hand B?

“I heard you have a new job, Dirk,” said Barney, taking a sip of his beer.

“Yea, I do, Barney, and it’s a really great job because I get a lot of time off to go fishing at the lake,” said Dirk Burton, master electrician, with a big grin on his face.

“Tell me all about it,” replied Barney – all ears.

“I’m working standby 24/7 for Acme Hot-Plug Electronics, Inc., a large company with many branches. They have an average of seven emergencies per week that they want me to handle,” explained Dirk, gulping down a large swig from his tall mug of beer.

“But that’s crazy, working 24/7. How do you get any time to go fishing?” asked an incredulous Barney, downing a big swig too.

“No problem, Barney. As the number of emergencies to be handled is logged by midnight, the next morning they let me know by 8 am via SMS how many there are for me that day. If they don’t need me, I get the day off,” explained Dirk, ordering another beer.

“I get it. You could get up to seven emergencies in a day, or none at all,” said Barney.

“That’s the deal,” said Dirk, “with no emergencies reported, I hang up my ‘GONE FISHING’ sign on the front door and head for the lake. From there I check the phone until they need me.”

“Wow, that’s the life,” exclaimed Barney filled with admiration, and finishing his beer, “got any fish for sale?”

Can you work out the probability that Dirk will have at least three days off during any week?

How many weeks, on the average, do you think Dirk would have to work to experience one single day with seven emergencies?

“I forgot to ask for your phone number, Julia,” shouted Roger desperately running after the bus that was pulling away from the airport terminal.

“It has three sixes, two two’s, and two nines,” shouted Julia back through the window as the bus accelerated beyond hearing distance.

Roger stopped running, pulled out a notebook, wrote down the information and began scratching his head.

Roger had been so absorbed in conversation with Julia since they sat next to each other on the plane, that asking for her phone number had completely slipped his mind.

Now to start dialing…

How many phone numbers will Roger have to dial to get hold of Julia?

“Daddy, what are these six colored balls for?”

“Well, son, you’ll notice that three of them are red, two blue and one is green. The red balls all have the number one printed on them, the blue balls all have the number two printed on them, and the green one the number three printed on it,” said daddy, holding up the balls.

“They have very pretty colors, daddy,” said Lenny, “so what do you have in mind.”

“Let’s see how many different six-digit numbers you can make, son,” replied daddy.

“I know already, daddy,” smiled Lenny, “but for the chemistry set you promised me, I’ll tell you how many numbers with digits from one to five can be made with these balls,” said Lenny enthusiastically.

“That’s certainly a deal, son,” said a nonplussed daddy.

How many distinct six figure numbers do you say can be made using these balls?

And, how many distinct numbers with one to five digits can be made with these balls?

Intriguing Puzzles Book 1 is now available for purchase here and on Amazon.

Intriguing Puzzles Book 1 contains 50 puzzles selected from the many puzzles on this blog and includes complete solutions and the mathematics you need to solve them.

Intriguing Puzzles Book 1 is divided into four sections: Puzzles, Hints, Solutions and an Appendix with mathematical information and procedures.

If you have wondered about the solution to a puzzle on this blog, you might discover the solution in Intriguing Puzzles Book 1.

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