One to One Marketing

It has been a while since my last post, this time it's not the usual rebus or puzzle... it's as gist of what Don Peppers and Martha Rogers said in their book 'Enterprise One to One'.
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Anagram

Find the four seven letter words. They are anagrams to each other.

1. It has paintings and pictures
2. It causes physical problems (say sneezing)
3. It is an adverb
4. In a manner relating to a monarch

Answers - May

Answers for Rebus post

1. Last laugh
2. Once in a blue moon
3. Once upon a time
4. Middle of nowhere
5. Forever a day
6. Get back to work
7. Just in time
8. Call a spade a spade
9. Time up
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Answer for Distance puzzle

Total distance traveled by soldier X is '20(2+sqrt(2))'
The sequence of diagrams below will help understand the solution better
Green line gives position of the battalion at a given time.
X, A and HQ gives the position of soldier, captain and Head Quarters respectively
All units are in miles

Stage 1: Distance traveled by Soldier = 0


Stage 2: Distance traveled by soldier = 20 + a
When soldier X meets captain A, the battalion would have covered a distance 'a' of the 20 miles towards their HQ. So X should have run the extra 20 miles from the end of the line to the beginning


Stage 3: Distance traveled by soldier = 20 + 2a
When X returned to his original position, A reached the HQ, meaning that they have covered the remaining distance (20-a). So, X should have run a miles in opposite direction in that time.

Stage 4 (last): Total distance traveled by soldier = 20 + 2a + 20
Having reached his original position, now X has to march another 20 miles to reach the HQ

Hence, X has traveled a distance of 40 + 2a miles in total
To find a: Use relative distance traveled by X and rest of the battalion
(20 + a)/a = a/(20-a)
Gives a = 20/sqrt(2)
So,
40 + 2a = 20 (2 + sqrt(2))

Distance puzzle

This is one of my favourite puzzles. Read it in 'Hard to solve math puzzles' by Derrick Niederman. I won't be reciting it word-by-word though

Captain A is leading a huge battalion marching towards their headquarters, which is 20 miles away. The battalion is so huge that it measured 20 miles in length. At this time, as they kept marching at a constant speed, soldier X, the man in the last row had to pass on a message to his leader (in person). He started running towards the leader who is in the first row of the battalion, met him before the leader could reach the headquarters, and again ran back to his position. When he did so, the leader reached the headquarters, the rest would follow.

So, what do you think is the total distance covered by the soldier when he reached the headquarters?
(You may ignore the time taken to convey the message)

Rebus

Spent time to draw these rebuses than to write. My favorite, the penultimate one. The idea just clicked while i was playing cards...

1. 
   
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 

I-post

I never knew what to write in a blog, but i wanted to have one
I named it 'safira to googol' because it gives an illusion as if my posts would cover literally everything under the sun :) though that's not going to happen at least for the time being, to say the least. Nevertheless, I'll occasionally share things that interest me.. numbers, puzzles, a few ramblings and so on.