Alpha Bit By Bit

E4
Consider these two sets of alphabets: AEFHIKLMNTVWXYZ and BCDGJOPQRSU. What can you attribute to them? Easy peasy. The first set can be drawn with straight lines while the second set cannot. Similarly, in HIOX and ABCDEFGJKLMNPQRSTUVWYZ, the first set has vertical symmetry while the second has horizontal. Fun and games over now because here it comes, six sets of letters from hell. Let's see if you can tell what distinguishes one from the other(s).
           
(1) ABEHIKMNOTXZ/ CDFGJLPQRSUVWY
(2) BDO/ P/ ACGIJLMNQRSUVWZ/ EFTY/ HKX
(3) CEFGHIJKLMNSTUVWXYZ/ ADOPQR/ B
(4) BCDIJLMNOPQRSUVWZ/ AEFGHKTXY
(5) COPSUVWXZ/ ABDEFGHIJKLMNQRTY
(6) EHIS/ MOT/ ABCDFGJKLNPQRUVWXYZ
 
DEAR MS
(The problem was: "What do you think the bacteria Lactobacillus bulgaricus and Streptococcus thermophilus have in common?" - MS)
 
Germ-Warfare Dept:
The answer for what is common between the bacteria Lactobacillus bulgaricus and Streptococcus thermophilus is that both are found in fermented milk products and are used in production of yoghurt. These bacteria are also known as lactic acid bacterium.
- Niraj Nandish, nirajnandish@icloud.com
 
These two bacteria have one thing in common: they are both the main (starter) cultures in yoghurt.
- Jaelyne Tauro, jaelynetauro@gmail.com
 
(The second puzzle was about discovering how two groups of 30 elements each were related, besides being anagrams of each other. - MS)
 
Elementary-My-Dear Dept:
The groups are related to each by the sum of the atomic numbers of the elements. When the atomic numbers are summed up, the result is 1,416, which is the same for both the groups of elements.
- Ibrar-ul-Samad, VJibi_94@hotmail.com
 
When you take each element and replace it with its atomic number and sum them up, the answer of both groups comes to 1,416. There's something really weird going on here!
- Dhruv Narayan, dhruv510@gmail.com
 
(The last one was given as an incomplete equation: "( ) / ( ) ( ) + ( ) / ( ) ( ) + ( ) / ( ) ( ) = 1. Distribute the nine digits 1 through 9 into the nine positions within the parentheses so that the equation is correct." - MS)
 
Days-Of-Toil Dept:
After toiling for two days, I was able to make out that the first fraction should be as high as possible and it works out to 9/12,which is 3/4th of 1. To account for the remaining 1/4 of 1, I jumbled the numbers and arrived at 5/34 and 7/68, which is the solution. Thanks for this mind-tweaking puzzle.
- Murali S L, murali_sl@yahoo.co.in

ENDGAME(S)
1. Consider working with a 12-slot centrifuge that has 12 equally spaced slots around a central axis in which chemical samples to be centrifuged can be placed. When the machine is turned on, the samples whirl around the central axis and do their thing. To ensure that the samples are evenly assorted, they must be distributed in the 12 slots such that the centrifuge is balanced evenly. For example, if four samples are to be used, they can be placed in slots 12, 3, 6 and 9 (assuming the slots are numbered from 1 to 12 like a clock). The question is can the centrifuge be used for five samples?
2. How many positive integers are there in which no digit occurs more than once?

(Mukul can be reached at mukul.mindsport@gmail.com)

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