Jump to content
Science Forums

Riddles


infamous

Recommended Posts

… hmmm interesting so... (9^9)^9 = 387420489^9 = 9^81 but does not equal 9^(9^9) …
…Compare 387420489^9 and 9^387420489.
I can’t resist the urge to interject something non-joking (perhaps even pedantic) into this thread:

In this age of wonderful electronic calculators, we should not forget the moldy old tools of estimation and logarithmic identities

 

base^(Logbase(n)) = n

Log(n^m) = Log(n)*m

 

Using the common (base 10) logarithm, Log(387420489) is about 8, so Log(387420489^9) is about 72, so 387420489^9 is about 10^72.

Log(9) is about 1, so Log(9^387420489) is about 387420489, so 9^387420489 is about 10^387420489. 10^387420489 is much bigger than 10^72, even allowing for my super-sloppy estimation.

Link to comment
Share on other sites

This riddle is an old common one you might remember from school and it is simple to solve;

 

You are given 5 bags. There are 10 beads in each of the bags. In four of the bags, the beads each weigh 10 kilograms. In the remaining bag, each bead weighs only 9 kilograms. All the bags and beads look identical. You must find out which bag has the lighter beads. The problem is that all the bags look identical and all the beads look identical. You can use a scale, but it has to be a single-tray scale, not a two-tray balance scale. Also, you may use the scale only once. How can you find out which bag has the lighter beads?

Link to comment
Share on other sites

Actually, never heard it before and it took some thinking to figure it out ;). I would label all the bags 1-5, then take out the same number of beads as the label on the bag said. Then place all 15 beads on the scale. Since most beads weigh 10 kgs, the weight should be close to 150 kg. But since at least one will weigh 9 kg, just subtract the actual weight from 150 and the number you have will tell you which bag contains the 9 kg beads ;).

 

(i.e. If it was bag three then three beads would weigh 9 kg and the other 12 would be 10 kg beads from the other bags. 12x10= 120(kg). 3x9= 27(kg). 120+27= 147(kg). 150-147= 3, the number of the bag from whence the 9 kg beads came from ;))

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
×
×
  • Create New...