**dan's math@home - problem of the week - archives****Problem Archives**page 10**Problems Only.**For answers & winners click here.**1-10****. 11-20 . 21-30 . 31-40 . 41-50 . 51-60 . 61-70 . 71-80 . 81-90 . 91-100****101-110****. 111-120 . 121-130 . 131-140 . 141-150 . 151+ .**prob index91- A Sinking Storm 92 - Tiling Me Softly 93- One for the Ages 94 - Hole In The Ball 95 - Above Avg. Art 96 - Missing Dollar ? 97-Three Funny Nos. 98 - The Dinner Date 99 - Birds on the Run 100 - Parents To Bee? - Problem #91 - Posted Tuesday, August 22, 2000
- That Sinking Storm ! (back to top)
- Fishing boat captains, when big storms form, behave as follows: 50% of the time they head for home, 30% of the time they choose to ride it out, and 20% of the time they head away from the storm. In a severe storm, the probability of being sunk is 97% if they head for home, 44% if they ride it out, and 17% if they head away. (i) What is the probability of being sunk? (ii) What is the probability that a boat was headed for home, given that it was sunk?
- Problem #92 - Posted Friday, September 1, 2000
- Tiling Me Softly (back to top) . . (Last problem of the 1999/2000 season.)
- Roberta and Lauryn want to tile their 20-ft by 21-ft floor, and they insist on using square tiles. The tiles are uncuttable, non-overlapping, and with integer sides. What is the smallest (total) number of tiles they can use, and what's the exact arrangement?*
- *You can attach a simple GIF file, or simply list the size of each square and the coords of its lower-left corner, starting with (0,0). More than one tile of the same size may be used, but tiles cannot hang over the edge.

- Problem #93 - Posted Sunday, September 10, 2000
- One For The Ages (back to top) . . (First problem of the 2000/01 year - our 4th season!)
- Macy and Tracy are friends whose combined ages are forty-four years. Macy is twice as old as Tracy was when Macy was half as old as Tracy will be when Tracy is three times as old as Macy was when Macy was three times as old as Tracy. How old is Macy? Be sure to include all your steps and reasoning!
- Problem #94 - Posted Tuesday, September 19, 2000
- Hole in the Ball (back to top) Another classic problem from my puzzling childhood!
- Did you see that wooden ball? It had a hole drilled clean through the center! The hole was five inches long; I dunno how big the sphere was, but I can calculate how much wood was left. What volume was left, and how'd I figure it?
- Be sure to include all your steps and reasoning for maximum ranking!
- Problem #95 - Posted Friday, September 29, 2000
- Above Average Art! (back to top)
- The graphics department at
dansmath.com has one artist and
**A**production assistants. Each assistant can make**B**illustrations per day, but the artist can make**C**more per day than the daily average of the whole department (including the artist). **1.**Find A, B, and C , given these clues:**A + B + C + 3 = (A!) / (5!) = (A^2 + AB) / 3 = 2C.****2.**What's the total production of dansmath.com, in illustrations per day?- . . A, B, C, and your answer should all be whole numbers.
- Problem #96 - Posted Sunday, October 8, 2000
- The Missing Dollar (back to top)
- Three guys walk into a hotel. The clerk says, "A room is thirty dollars." Each guy gives the clerk ten dollars. The men go to their room; the clerk remembers the room is only twenty-five dollars. She gives the bellboy five singles to give back to the men. The bellboy can't decide how to split five among three men, so he gives each man one dollar and keeps the other two for himself. Now: The men have payed nine dollars each for the room. Three times nine is only twenty- seven, and with the two the bellboy has, that makes twenty-nine. Explain clearly: Where did the other dollar go?
- Problem #97 - Posted Tuesday, October 17, 2000
- Three Funny Numbers (back to top)
- The first funny number: If a 1 is placed after this five-digit number, the result is triple the number you'd get by putting the 1 in front. The second funny number: It's the second-smallest odd number greater than 1 that's a perfect cube and also a perfect square. The third funny number is the smallest with the property that if any prime between 10 and 20 is divided into it, the remainder is 1. What's the exact product of the three funny numbers?
- Tell the 'whole' story: give the entire answer and show how you got each step.
- Problem #98 - Posted Wednesday, October 25, 2000
- The Dinner Date (back to top)
- That 'Math Council Dinner' is in December, but I forgot which night, so I asked around. Alan said that the date was an odd number; Brenda claimed it was greater than 13. Carly declared it was not a perfect square, while Dara swore it was a perfect cube. Finally, Edward told me the date was less than one-fourth his age, which I know to be 68. Yesterday I learned that only one of them had told the truth! What is the date of the dinner?
- Problem #99 - Posted Friday, November 3, 2000
- Birds on the Run? (back to top)
- Someone opened up the cages at the pet shop, and over 100 birds got away! There were exactly 300 birds to begin with. The local paper (the Daily Poop) reported: "Of the birds that remained, a third were finches, a quarter were budgies, a fifth were canaries, a seventh were mynah birds, and a ninth were parrots. The original number of canaries was three times the number of parrots that stayed." The reporter got just one of the fractions wrong. How many canaries escaped?
- Problem #100 - Posted Saturday, November 11, 2000
- Parents To Bee? (back to top)
- Every male bee has just a female parent, while every female bee has both a male and a female parent. How many ancestors does a male bee have counting ten generations back? Twenty? Don't count this male as a generation or include him in the 'final tally.'
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