Math Puzzles for February 2000

February 27, 2000 An ant is crawling at a rate of one foot per minute along a strip of rubber which can be infinitely and uniformly stretched. The strip is initially one yard long and one inch wide and is stretched an additional yard at the end of each minute. If the ant starts at one end of the strip of rubber, will it ever reach the other end, and if so when?
Answer:
Many people answered 11, which is close, but I believe I stumped everyone on this one!		 The ant does reach the end of the strip of rubber, in about 10 minutes and 47 seconds.
During the first minute, and before the first stretch, the strip is 3 feet long and the ant travels 1 foot, so it travels 1/3'rd of the way down the strip. During the second minute, after the first stretch but before the second one, the strip is 6 feet long and the ant travels 1 foot, so it travels 1/6'th of the way down the strip. In general, during the n'th minute, the strip is 3n feet long and the ant travels 1 foot, so it travels 1/3n'th of the way down the strip. The first question, whether it ever reaches
the end of the strip, is answered by observing that the sum 1/3 + 1/6 + 1/9 + 1/12 + ...
will eventually exceed 1; in fact, the last time it's less than 1 is at 1/3 + 1/6 + 1/9 + ... + 1/27 + 1/30 which is about 0.9763.
So, after 10 minutes the ant has traveled about 97.63% of the way down the strip, the strip being 33 feet long at that time (after
the stretch).
When exactly does it get there? It took the ant 10 minutes to travel first 97.63% of the way. The ant had about 33(1 - .9763) feet to go and, since it travels 1 foot per minute, it reaches the end in about another 46.88 seconds.
   
February 20, 2000 1.  Substitue numbers for letters so that you create a correct addition problem:

         a
+   bbb
+   bbb                     There are 3 possible answers.
+   bbb
+   bbb
    abbb
                   

2. In what mathmatical equasion must you write the number 3 to equal 4? (EASY!)
Answer:
Dusty Grundmeier		      1          2          3
+333   +666   +999
+333   +666   +999
+333   +666   +999
+333   +666   +999
1333    2666   3999

Question 2:
3/3+3=4
   
February 14, 2000 My three nieces are coming to visit. My neighbor came over and wanted to know how old they are. I told her that the product of their ages is 72.

"That's not enough information for me to figure out how old they are," she complained.

I offered that the sum of their ages is my street address.

"But that's still not enough information."

After a moment's thought, I added that my eldest niece loves pizza.

She then knew how old the girls are,...but was afraid to ask their names.

How old are my nieces?
What is my street Address?
Answer:
Dusty Grundmeier		 Since the product of the ages is 72, the ages must be among the factors of 72. This gives the following possibilitites.
First Age Second Age Third Age Sum of Ages
1 1 72 74
1 2 36 39
1 3 24 28
1 4 18 23
1 6 12 19
1 8 9 18
2 2 18 22
2 3 12 17
2 4 9 15
2 6 6 14
3 3 8 14
3 6 4 13

Since knowing the sum of the ages did not uniquely identify the ages of the nieces, you must conclude that the sum of the ages is 14, as no other sum appears more than once. The final information about the likes of the eldest niece tells the neighbor that there is an eldest niece, which would not be the case if the nieces ages were 2, 6 and 6. The only remaining possibility is that the nieces are 3, 3 and 8, and that incidentally, the house number is 14.

   
February 7, 2000

Four Scouts have to cross a dangerous bridge to get to their campground. It is nighttime and they have one candle between them which will burn for a mere 17 minutes after it is lit. If the candle goes out once lit, they have no way to re-light it.
The bridge will hold at most two Scouts at a time, and each crossing must take place with the lighted candle. The candle must be walked across with each group; it cannot be thrown, for example, as it would go out. Each Scout walks at a different rate, and any two Scouts walking together must walk at the rate of the slower camper's rate. The Scouts walk at the following rates:

M.J.
1 minute to cross		 Ollie
2 minutes to cross
Libin
5 minutes to cross		 Kathy
10 minutes to cross

Can they make it across?  And if so, how?
Answer:
Dusty Grundmeier		 M.J. and Ollie cross the bridge taking 2 minutes.
M.J. Goes back across
M.J. gives the candle to Libin and Kathy they cross taking 10 minutes.
Ollie goes back across taking 2 minutes
M.J. and Ollie cross together taking 2 minutes.
Everyone is ACROSS THE BRIDGE