Civil engineers need to design around people. This is a hint for this week’s Micro Softy. 

At the Dallas-Fort Worth (DFW) airport, the train Skylink seamlessly transports you from terminal to terminal. Trains depart every 2 minutes, with a maximum travel time of 9 minutes between the farthest points, making it highly efficient. The train operates from Level 3. An up escalator takes you there. 

Here is something interesting. There is a single escalator that takes you up to the Skylink train. There are two down escalators for those exiting the train. That’s this week’s Micro Softy. Why are there two down escalators but only a single up escalator for Skylink?

See next week’s Micro Softy for the obvious answer. 

Solution to Micro Softy 73: Necklace Cutting  

Here’s last week’s Micro Softy concerning a girl named Sally with money flow problems.  

Sally needs to pay her rent daily for 30 days using individual gold beads from a 31-bead necklace. However, each time she cuts the necklace to separate beads, she must pay a jeweler to reconnect it. To minimize these jeweler fees, she must find a strategy that allows her to give the landlord exactly one bead per day using the fewest possible cuts. What is the minimum number of cuts required to achieve this? 

The minimum number of cuts Sally needs to make is 4. 

Here’s how it works: Sally can cut the necklace into segments of beads in powers of two: 

• 1 bead 
• 2 beads 
• 4 beads 
• 8 beads 
• 16 beads 

These five segments total 1+2+4+8+16=31 beads. So, she has all 31 beads available, split into five segments. 

Each day, Sally gives the landlord the right combination of segments to add up to the total number of days passed — just like how binary numbers work: 

• Day 1: give 1 
• Day 2: take back 1, give 2 
• Day 3: give 1 (now 2 + 1 = 3) 
• Day 4: take back 1 and 2, give 4 
• Day 5: give 1 (now 4 + 1 = 5) 
• … 
• Day 30: landlord holds the 16, 8, 4, and 2 beads (16 + 8 + 4 + 2 = 30) 

So Sally needs to make only 4 cuts to create 5 segments (cutting the necklace into 1, 2, 4, 8, and 16-bead chunks). She gives and receives segments as needed to ensure the landlord has exactly one more bead each day. 

For fellow nerds, here’s a more mathy description using binary numbers. By using powers of two, every number from 1 to 31 can be represented.  The above table can be written using binary numbers as: 

• Day 1: 00001  One bead 
• Day 2: 00010  Two bead strand 
• Day 3: 00011  Two bead strand + One bead 
• Day 4: 00100  Four bead strand 
• Day 5: 00101  Four bead strand + One bead 
• … 
• Day 30: 11110 Sixteen bead strand + 8 bead strand+ 4 bead strand + 2 bead strand 

So, hooray for binary numbers! 

The Monday Micro Softy is a weekly feature of Mind Matters News. Here are the links to all the puzzles and answers to date:

Monday Micro Softy 72: Necklace Cutting required knowledge of binary numbers. Keep this in mind to work out the minimum number of cuts that allows Sally to give the landlord one bead a day for a month. You can find puzzles 55 through 72 here as well.

Monday Micro Softy 71: Strange Economics required you to grasp the deeper meaning of overheard conversations between a customer named Bill and a store clerk in a hardware depot. The question is: What was Bill buying? You can find puzzles 55 through 71 here as well.

Monday Micro Softy 70: The light above your stairs involved the Switching Theory and how a two-way switch works. If the stair light is on, flip the downstairs switch and the light goes on/off. A flip of the upstairs switch does the same thing. If the light is off, flipping either switch turns the light on.  What’s a simple circuit that does this?  You can find puzzles 55 through 70 here as well.

Monday Micro Softy 69: A Bunch of Switches involved knowledge of Switching Theory. Last week, Frenchy and the other prisoners at Pokey Nook Prison flipped a switch each day for 101 days, On the 102^nd day, Frenchy announced with certainty the 101^st prisoner had arrived. How did he know? You can find puzzles 55 through 69 here as well.

Monday Micro Softy 68: An Overcrowded Prison featured Frenchy and the other prisoners at Pokey Nook Prison, who flipped a switch each day for 101 days. On the 102^nd day, Frenchy announced with certainty the 101^st prisoner had arrived. How did he know? You can find puzzles 55 through 68 here as well.

Monday Micro Softy 67: Three Switches and a Song was about switching theory. Wide Clyde wants to go upstairs to cook some Top Raman noodles. To do that, he needs to identify which of three switches controls the hot plate upstairs. The hot plate is plugged in but currently off. The other two switches turn outside lights off and on. Wide Clyde can’t see outside, so he can’t determine which switches control the lights. How can Wide Clyde determine which switch controls the hot plate with just one trip upstairs? You can find puzzles 55 through 67 here as well.

Monday Micro Softy 66: Reducing Repetitive Repetition requires being BFF’s with numbers, and last week’s Micro Softy was tough and mathy. Here is the solution: Any three-digit number multiplied by 1001 duplicates the number. For example, 214 x 1001 = 214,214. And 13 x 11 x 7 = 1001. So dividing the big number by 13, then 11 and then 7 is the same as dividing by 1001. The original three-digit number always results! 

Monday Micro Softy 65: Fathers and sons was about two fathers and their two sons who walked into a Bass Pro Shop in Memphis, Tennessee. Each man bought an AK47 rifle with ammunition and a 75-round drum magazine. But all together, only three AK47’s were sold. How could this be? The solution is there were altogether two fathers (father and grandfather) and two sons (the father and his son) but only three men. You can find puzzles 55 through 65 here as well.

Monday Micro Softy 64: Old Time Phishing was about an investment banker, Geardown Geko, who received anonymous tips forecasting the outcome of future events starting in 1948. The solution is: The winner of Tipper’s phishing lottery. It was a type of phishing where in the end there was a single winner participant, Geko. Someone had to win. Everyone else who bet on the predictions eventually was a loser. You can find puzzles 55 through 64 here as well.

Monday Micro Softy 63: A Beggar’s Tale. Exceptional nerds are psychologists who see through surface actions. Such a skill is required to solve this Micro Softy. The solution to Freaky Bob’s strategy is: If he had taken the $10, he’d have lost repeat customers. Nobody would’ve been entertained. Choosing the $5 kept people coming back with more cash, proving far more lucrative for him in the long run. You can find puzzles 55 through 63 here as well.

Monday Micro Softy 62: The Ordeal of Sisyphus Fats. The best computer programmers and engineers must be good at scheduling. Last week’s Micro Softy tests this ability and the solution is that Sisyphus Fats took 98 minutes to push the large bowing ball to the top of the 100-foot hill. You can find puzzles 55 through 62 here as well.

Monday Micro Softy 61: Micro Softy Take Five was more of a trivia question than it was a puzzle. To solve Micro Softy 61, the answer is the theme for the Mission Impossible movie franchise starring Tom Cruz. You can find puzzles 55 through 61 here as well.

Monday Micro Softy 60: Here’s a puzzle from Gunsmoke Told to “get out of Dodge”after a shooting, a gunslinger does so at a nearly inexplicable time. Can you solve the puzzle?
To solve Microsofty 59, recall that direction of air flow is due to pressure — not size. Which tire is under more pressure? You can find puzzles 56 through 59 here as well.

Monday Micro Softy 55: “It happens every spring.” Baseball, that is. Here’s a puzzle that takes in baseball’s summer. To solve last week’s puzzle, you don’t need to know the distance. Check the problem again for the number you do need to know. You can find puzzles 51 through 54 here as well.

Monday Micro Softy 50: Cutting through the cornbread. How did Yuri Senior cut the cornbread into eight identical portions using only three straight cuts? You can guess the answer to Microsofty 49 if you try the test question yourself at home, using a small mirror. Links to Microsofties 46 through 49 are here as well.

Monday Micro Softy 45: Can Tony beat the fast-food curfew? An early curfew on fast food service motivated a boy to exercise more vigorously. But how fast was he pedalling? To solve Micro Softy 44, recall that Tony doesn’t need to take the individual pills each day, only the prescribed amount of each. You will find links here to Micros Softies 41 through 44 as well.

Monday Micro Softy 40: The fate of a false prophet. He wasn’t actually fired for being a false prophet but for something that his prophecy unintentionally revealed. The solution to Micro Softy 39 lies in considering an alternative possible meaning of a word commonly used in sports. You will also find links to Micro Softies 30 through 39 and their answers here as well.

Monday Micro Softy 29: A funeral lament in four lines. The funeral director was puzzled by Dan’s description of his relationship to the deceased but there was no question that his grief was sincere Here, you will also find links to Microsofties 22 through 29.

Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills. Here, you will also find links to Microsofties 11 through 20 as well.

Monday Micro Softy 11: What Happened to That Other Dollar? Here you will find links to the first ten Micro Softies. Have fun!