Summary: Jan/Feb 18 – Brain Teasers

Jan/Feb ’18 Brain Teasers – SUMMARY

REMINDER: Answers in red.  Solvers (submitted/correct) in blue. (Forgive any omissions.) Comments in green. For further elaboration, feel free to ask! 

• 1. Answer either or both:  If you could spend $1 a minute, how long would it take you to spend $1,000,000? 1 year, 329 days 10 hours and 40 minutes  If you spent a $20 bill a minute, how long would it take to spend one billion dollars?   . 95 years 47 days 320 minutes.  I got a VARIETY of ‘precision’ here, but most answers got most of the credit.  Jim Waterman, Alexis Avis (part a), Jennifer Steele.  Partial credit to Amy Ragsdale.
• 2. A bottle of old brandy costs $45.  The brandy costs $40 more than the empty bottle.  What is the cost of the empty bottle?  $2.50 [Not $5].  (Then Brandy costs $42.50). Jim Waterman, Alexis Avis, Jennifer Steele, Amy Ragsdale.
• 3. James says “I have as many brothers as sisters.”  His sister says, “I have twice as many brothers as sisters.” How many brothers and sisters are in this family? Four brothers and three sisters (total 7).  That way each brother, including James, has 3 bros and 3 sisters,  Each sister has 4 bros and 2 sisters.  Jim Waterman, Alexis Avis, Jennifer Steele.
• 4. How many 3-digit numbers have all odd digits?  125. Is the answer the same for all even digits? No. (Only 100). Jim Waterman, Alexis Avis, Jennifer Steele, Amy Ragsdale.
• 5. Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday Friday, Saturday, or Sunday, or any of the months of the year? One solution is Yesterday, Today, and Tomorrow.  (Most submitted other – correct – answers.) Jim Waterman, Jennifer Steele, Amy Ragsdale.
• 6. A man and his son are in a car wreck, and are taken to different hospitals.   At the emergency room of the hospital where the boy was taken, the attending physician gasps and says ” I can’t work on this patient – he’s my son!”  How can this be? The doctor is the boy’s mother.  Jim Waterman, Alexis Avis, Jennifer Steele.
• 7. This is an unusual paragraph.  I’m curious how quickly you can find out what is so unusual about it.  It looks so plain you would think nothing is wrong with it.  In fact, nothing is wrong with it!  But it is unusual, though.  Study it, and think about it, but you still may not find anything odd.  But if you work at it a bit, you might find out.  Try to do so without any coaching!  The paragraph does NOT contain the letter ‘e’ at all. Amy Ragsdale.
• 8. Ralph is trying to limit his coffee input, so he alternates days of drinking coffee and hot tea. He drinks coffee on odd-numbered mornings, and hot tea on even-numbered mornings.   Further, he always allows himself coffee on Mondays, regardless of date.  He’s discovered that under these conditions, there are occasionally circumstances in which he could drink coffee for four straight days.  Can you deduce those circumstances? Any 31-day month where the the last Saturday is EITHER the 28th OR the 31st. Jim Waterman, Alexis Avis, Jennifer Steele.
• 9. FUN FACT. How many total minutes will there be in this month (February 2018)?  (Note:  This BT is similar to [and perhaps easier than?] #1 above, but it’s here for a special reason.  The answer reveals a neat new FUN NUMBER FACT!) (Emphatic Hint!  The answer involves the number 8!)   40,320.  But see elaboration below.   Alexis Avis, Jennifer Steele, Amy Ragsdale.
• 10. Which number has more total divisors:  60 or 160?  Turns out they both have the same number – 12.  (Not sure I intended that when I started 🙂 ). Alexis Avis, Jennifer Steele, Amy Ragsdale.
• 11. Carpet is being advertised for $11.99 per square yard.  (Call it $12 if you’d rather.) How much will it cost for the carpet only to fully carpet a small 9′ x 12′ bedroom?  (As with most fake word problems, you may ignore costs of padding, labor, tax, etc.)   9ft x 12ft is the same as 3yds x 4 yds.  The room, then, needs 12 square yard, so the cost would be $144 (or $143.88)        Alexis Avis, Jennifer Steele, Amy Ragsdale.
• 12. FUN FACT. An Antarctic base reports the temperature as ‘forty below zero’, but neglects to note whether that’s Fahrenheit or Celsius.  Obviously, these are both COLD, but which is colder?  Neither. This is the one place where the temperatures are the same on each scale.  (You can mathematically verify this with either/both of the formulas.  Holler if questions.) Alexis Avis, Jennifer Steele, Amy Ragsdale.

Problem 9 Elaboration: 

28 days, each with 24 hours, each with 60 minutes.  So the ‘answer’ is 40,320. 
But that answer also happens to be 8! (eight factorial), which is defined as  8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.  To see this, you can note that 28 x 24 x 60 = (7×4) x (8×3) x (6x5x2).  Rearrange those and you get the above.
So the HINT in #9 above (‘the answer involves the number 8!) was simultaneously the most obvious and the most misleading clue I could have given!)