Questions 0
Answers 11


The contestants in a chess tournament were numbered from 1 to 18. When the players were paired for the first game, the sum of the two numbers for each pair was a perfect square. What were the pairings for the first game?

I remember these from one of my logic puzzle books a couple of years ago. It real easy to do.

You have to make a chart like this. 1/2 chart really but I made the whole thing because you can see it easier.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 x---4---------9---------------------------16
2 -x-----------9------------------------16
3 --x------9-----------------------16

Then where the row and column intersect put in the sum.

Then erace all numbers that are not perfect squares or just put only those in the first place'

Mark off all matchin numbers because a person cant play with himself -- tho when i do I always win the game (haha)

Notice there is only one way to make a 4 so remove all number on row 1 because you can only use them once the numbers removed are 9 and 16
There is only one in each collom any way so you don't have wory about removing them.
Then make a list to keep track like I did at the bottom.
4 is the only one by it self so 1 and 3 have to be used for this.
16 is the only one on the 2s row so we have to use 2 and 14.

keep track list
4(1,3) 16(2,14) 16(4,12) 16(5,11) 25(7,18) 25(8,17) 25(9,16) 25(10,15) 25(12,13)

These are the answers

This is the first question I answered here.

by Puzzled

PS I saw The Dumb Guy answer and your not dumb if you can do this.

the only difference is the way I did it includes the perfect square of 4.

Puzzled Jan 27, 2014
Hi Melody

I played the logic puzzle game you told us about. I haven't figured it out yet. Its a real hard one. I made it more than 1/2 way through mostly by dumb luck. It starts over when you make one mistake.

My name is Michelle and my nick name is the same as yours its Melody . My Dad gave it to me when I was 9. Its a funny story how I got it. I like the name and some of my friends back home call me Melody. I picked Puzzled as user name because I love puzzles.

I'm glad someone solve the magic number puzzle. I wounder how long it took him. One of them took me 3 days. I probably could have done it faster if I didn't have a ton of homework.

I decided to try your new puzzle what is a number divisible by.

67960350 is divisible by

10 because of the 0 at the end (rule 2)
2 because it is even (rule 3)
It's not prime because it is even.
divisible by 5 it ends in 0
divisible by 3 if the sum of its digits is exactly divisible by 3
divisible by 9 if the sum of its digits is exactly divisible by 9
not divisible by 4 because the last 2 digits are not a multiple of 4
not divisible by 8 because the last 3 digits are not a multiple of 8.

I don't know what Zamarronics's formula is. I Googled it and all that came up was preserving love energy and other weird mumbo jumbo. No math formulas though. Does it have a different name?

I read DavidQDs divisor solution and decided to practice with it, because this is coming up in the next week or so in my class. I always read ahead in the text book.

I know your rules said not to use a calculator, but after factoring out one 2, and three 3s, and two 5s, I had 50341 left over. After dividing it by the next 10 primes I figured it might be prime so I used the calculator to test it and it is.

67960350 = 2*3^3*5^2*50341

It took me a while to do it because I was doing it backward and wrong like this.

67960350 =2*3*3*3*5*5*50341 --->1,2,2,2,4,5,5,50340

Then I thought I should have added 1 to each because I am trying to find the number of divisors a number has instead of what number has this many divisors.

67960350 =2*3*3*3*5*5*50341 --->3,4,4,4,5,6,6,50342

And that is still wrong. If not for the big number at the end I might still be doing it wrong.

That's when I thought its the exponents we count not the prime numbers.

67960350 = 2*3^3*5^2*50341 ---> 2,4,3,2 This looked much better and I remembered to add 1.

Then I multiplied the numbers to gether and got 48. So there are 48 numbers that will divide into 67960350 with
a 0 remainder. I don't know how to get the divisors though.

Now that I know there are 48 divisors I used Davids example to see if there is a smaller number that has 48 divisors.

48 = 2^4*3 =2*2*2*2*3 --> 1,1,1,1,2 ---> 2^2*3*5*7*11= 4620
48 = 2^4*3 =4*2*2*3 --> 3,1,1,2 ---> 2^3*3^2*5*7 = 2520

I stooped here because making the 2 bigger with a 4 exponent is more than the 7 it would replace.

This is so cool. I wish I could give him a big hug! I read the section in my book many times and couldn't get it. Well its an E-reader not really a book and I can print the pages if I need to. But it didn't explain it good. The $&#*#^! battery keeps going dead too.

I read his ladder answer too. I know how to do basic Trig but I don't understand this yet. I've got a loooooog way to goooooooo. Not just in math but English too. My teacher says my writing is atrocious. I laughed because my mom uses that word. It would be worse if it wasn't for spell check.
All my life everyone told me how smart I am. Now I know how dumb I can be sometimes.

When I was little my Dad told me the sun rises in the west in Australia. It was easy to get my brothers globe and picture myself standing in Australia and tell that the sun rises in the east. But he also said the water goes down the drain counter clock wise because the earths relative rotation is reversed. That was easy to see with the globe too. My Dad likes to kid and he also knows I will look things up to make sure he's rite or prove him wrong that's usually why he said these things.

But the water swirling down a drain I don't really know. I've watched a lot of drains (i like the little tornadoes) and most go clock wise but I've seen some go counter clock wise. The thing is up here the earth spins counter clock wise so I would think the water would swirl counter clock wise here and clock wise in Australia. Most people I've asked says it is opposite but weren't sure which was which. Have you ever noticed this? Or is it folklore?

Thank you
Bye for now.

Michelle a little less Puzzled, but still curious.
Puzzled Jan 26, 2014