January ’16 Brain Teasers

1.  Answer either or both:  If you could spend $1 a minute,  how long would it take you to spend $1,000,000?  If you spent a $20 bill a minute, how long would it take to spend one billion dollars?
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?
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?
4. How many 3-digit numbers have all odd digits?  Is the answer the same for all even digits?
5. Last month (see DecBT, #6), we encountered a problem where a piggy bank started with 2 cents in it and you doubled that amount each day.  At the end of ONE week, there was $1.28 in the bank.  If you were to continue that process (doubling the current amount with that day’s deposit), how much would be in the bank at the end of TWO weeks?
6. Notice that 2 + 2 = 2 x 2.  Can you find three whole numbers whose sum also equals the their product?  (Mini-Bonus:  If you’re allowed to use integers [negatives included], can you find three more?)
7. Suppose you have a 7-minute sand timer and an 11-minute sand timer.  What is the easiest way to time the boiling of an egg for 15 minutes?
8. CONTEST? Using each of the 10 digits ONCE, find two different 5-digit numbers that have the largest product.  (Let’s also make this an ongoing contest – start somewhere and send in your best current answer whenever you have one, and we’ll keep track of the current record [and all submitters] weekly.  I’ll keep us posted.)  UPDATE 1:  Jim Waterman submits 97531 x 86420, which = 8,428,629,020, and is the CURRENT RECORD.  Thanks, Jim.  Who’s next?  (I believe there is at least one possibility with a higher product, maybe more.)

9. Jack is lighter than Phil, but heavier than Bob.  Bob is lighter than Jack, but heavier than Pete.  Which man is the heaviest, and which man is the lightest?

10. Gloria is making 97 packages for a party.  How many packages does she need to buy, if the sandwich rolls come in pkgs of 8?

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EXPLORATION/BONUS

EXPLORE FOR FUN: Take a calculator and enter any six-digit number.  Hit the “square root” key until there is a ‘1’ before the decimal point.  How many times did it take?  Try it again (and again).  What do you find?  Interesting, eh?

BONUS 1:  Can you explain this phenomenon?

BONUS 2

Do you remember the cartoon from Jan 4?  Check it out again here:  LogiciansInBar. Explain how the 3rd logician knew that they all three wanted a beer.  (This is NOT as hard as these problems usually can be.  Give it a shot!)

EXTRA (Mini?) BONUS

There’s a fun problem revealed in a recent column in the Springfield News Leader.  To see it, visit Colm&Prob.

 Submit Answers!  There are NO tests and the answers are NOT graded, so lighten up!  If you want to submit  your answers to any or all of these, PLEASE feel free to do so!!  

You can always do this 3 ways:  1)  Use the Leave A Reply section below (though I may not make it public until after the deadline);   2) reply to (or contact) me directly by e-mail or by replying to any Weekly Sharing; or 3) by using the Contact Form link.   

Reminder:  Official deadline for  ALL BT submissions in January is noon, Thursday, Jan 28. (Late submissions accepted if Answer Sheet hasn’t been prepared/posted, but no promises.) Solutions will appear on Monday, Feb 1.