Brain Teasers Posted Fall ’16
(For a look at all previous BTs and Solutions/Submitters, see BT1).
REMINDER: Answers in red. Solvers (submitted/correct) in blue. (Forgive any omissions.) Comments in green. For further elaboration, feel free to ask!
1. A young tot answered the phone and asked who was calling. “I married your mother, but I am not your father – or your stepfather!” the man replied. Who was calling? The man officiated at the tot’s parents’ wedding. Dennis Newkirk, Dan Felshin, Jim Waterman, Jennifer Vise, Denise Griffin.
2. Using only pennies, nickels, dimes, and quarters (but at least ONE of each), make change for $1.00, using exactly fifty coins. 1 quarter, 2 nickels, 2 dimes, 45 pennies. Dennis Newkirk, Dan Felshin, Jim Waterman, Jennifer Vise, Denise Griffin.
3. A digital clock forms palindromic numbers* 114 times a day. What is the least time between two consecutive palindromic clock numbers? What is the most? Least: 2 minutes between 9:59 and 10:01. Dennis Newkirk. Most: 70 minutes between 11:11 and 12:21. Dennis Newkirk, Jim Waterman, Denise Griffin.
4. Ralph drives 60 miles at an average speed of 30 mph (fog maybe?), then returns over the same route at an average speed of 60 mph. What is his average speed for the entire trip? 120 miles traveled in 3 hours, so 40 mph. (A quick, common answer of 45 mph is a reminder that you ‘can’t average averages’ !) Dan Felshin, Jim Waterman, Denise Griffin
5. What are the next two letters in this sequence? O, T, T, F, F, S, S, ___, ___. The ‘intended’ (not necessarily the only correct) answer is E, N. (Letters form first initials of first counting numbers. 🙂 ). Jennifer Vise, Denise Griffin
6. A wooden cube is dropped into red paint. It is then cut into 27 equal-size smaller cubes (2 cuts each direction, like a Rubik’s Cube). How many of the smaller cubes are found to have red paint on a) 3 faces, 8 (the corners) b) 2 faces, 12 (middle cubes on each ‘edge’ row) c) 1 face, 6 (middle cube on each face) and d) no faces? 1 (the innermost ‘hidden’ cube) Jim Waterman, Jennifer Vise, Denise Griffin
7. Which is more: The product of the integers from -5 to 5, or the sum of those same integers? Neither. Both the sum and the product are 0. Dan Felshin, Denise Griffin.
8. a) Find the sum of the reciprocals of the first four primes. 1/2 + 1/3 + 1/5 + 1/7 = 247/210. (= 1 37/210) b) Is that sum more or less than the product of the same four numbers? Considerably more. Product = 1/210. Denise Griffin
9. Fill in the blank below with the symbol for one of the four standard arithmetic operations in such a way that the answer is a) The largest +; (1.8) b) the smallest – ; (0) Jennifer Vise, Denise Griffin
0.9 ___ 0.9
10. Find a number between 3/7 and 4/9. Infinite number (literally) of correct answers here. (Just one of them is 7/16*. Another is 55/126. Also any decimal between .429 and .444. And others.) Jennifer Vise, Denise Griffin
*This one is fascinating, as it happens to be the sum of the numerators (3 + 4) over the sum of the denominators (7 + 9)! Interestingly that trick will always work!!!
11. Sam goes to the bank to get an equal number of dimes and quarters. On the way home he spent 3 quarters and 1 dime, leaving him 52 coins. What is the total value of all the dimes and quarters Sam got from the bank? Sam left the bank with 28 of each coin or $9.80 Jennifer Vise, Denise Griffin
12. The first 10 numbers in the sequence 3, 33, 333, 3333, . . . are added. What is the digit in the thousands place of the answer? It’s a 3! Jennifer Vise, Denise Griffin
