NOTE: All submissions to any of these BTs receive an entry into a drawing for a free 2017 Calendar of your choice. Correct submissions receive at least one more.
1A. There are several interesting facts/traits surrounding the number 2017. Share one or more that you find. (NO ‘wrong’ answers here!)
1B. One special date in 2017 is 1/17/17. It is the only “Year-Product-Day” [YPD] this whole year! Can you define (or guess) what a YPD is? If so, when will the next one occur? When is the next year with only one YPD? When is the first year this century without a YPD? (Hint: We haven’t had it yet, if at all.)
2. Find a 5-digit number where the sum of all the digits is 25, and each digit is 2 more than the digit preceding it.
3. What number is 20 more than twice the number that is 10 more than 15 times one-half of ten?
4. Counterfeit Coin, Part 1 You have 12 coins in front of you, knowing that one of them is counterfeit. All you know is that the ‘bad’ coin is slightly heavier than the others. You also have a balance scale in front of you, and your task is to determine the ‘bad’ coin using only three (3) weighings*. How do you accomplish this?
*A weighing occurs any time you set something on both sides of the scale.
5. Miss Demeanor often goes the wrong way on a one-way street – RIGHT PAST a police station. How does she manage to do this without ever getting a ticket?
6. Find three consecutive integers that have the same product as sum.
7. Find a fraction which is equivalent to 1/2 and whose numerator and denominator have a product of 72.
8. Find the smallest positive integer which is divisible by each integer from 1 to 10 inclusive.
9. Fill in the missing letters: I V X __ ___ D M.
10. Consider a 7 x 7 x 7 stack of smaller cubes, all of the same size. How many of these are totally hidden from view?
11. You are facing south. You turn left, make an about-face, turn right, and then turn right again. Which direction is behind you?
12. (All names are street names.) Belvedere is parallel to St. Anthony. Davidson is perpendicular to River, which is parallel to St. Anthony. Is Davidson parallel or perpendicular to Belvedere?
BONUSES
All (legitimate) submissions to any of these Bonus BTs receive an entry into a drawing for the Rollin’ On The River book when it is released. All correct answers receive at least one more. (Numbers at the end of each BT represent maximum possible entries to be awarded.)
A. Counterfeit Coin – Part 2 Same situation as #4 above. Twelve coins, one is counterfeit, but you don’t know if it’s too light OR too heavy. You still have (only) 3 weighings to determine the bad coin. NOTE: It can be done, but it takes some clever thinking. (Solutions will need to explain carefully for full credit.) [3]
B. (See #1B above for details.) What is the only year (last two digits) each century that has seven (7) Year-Product Days? [2]
C. (See #8 above). Find the corresponding smallest integer divisible by each integer from 1 – 20. [2]
D. In #10 above, how many of the cubes have only 1 face visible? [2]
E. Here’s a fun BT I posted a year or so ago, and didn’t get too many nibbles. It’s not as hard as it might look, so I’ll pitch it out again. See 3LogiciansBar. [2]
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