Roses in May

E4
Your friends, Rose and May, both live on the sunny side of Woodland Grove in a row of five houses. You know that May lives with her parents, Mr and Mrs Joiner, in the house called 'The Oaks', but Rose has never told you her surname or the name of her house. Now you want to send both of them invitations to your 21st birthday party. So you ask the local newspaper delivery guy if he knows which house Rose lives in or the name of her parents. He's not sure, but comes up with the following facts:
(1) Each of the five houses is occupied by a married couple with one unmarried daughter. (2) The last of the five houses on the right is called 'Fir Trees'. (3) The Turner family lives in the house immediately to the right of the house called 'The Willows'. (4) The Carpenters live next door, but to the house called 'Silver Birches'. (5) The second house from the left is the home of the Sawyer family. (6) Cherry is the daughter of the couple in the middle house. (7) Ivy lives with her parents at 'The Elms'. (8) Hazel is the daughter of Mr and Mrs Woodman. From this info you should be able to deduce Rose's surname and the name of her house.

DEAR MS
(The problem was: "Let's call it a 'triad' whenever three people are all mutually interrelated or totally unrelated. How can you show now that in a set of any six random people, who may or may not be interrelated or unrelated, there is, nonetheless, at least one such triad?" - MS)
 
Relative-Density Dept:
Divide the people into partitions such that all people in a partition are related to each other and a person not in a partition is not related to any person in that partition. Now it's easy to see that either there will be three or more partitions or there will be at least three persons in at least one partition. In the first case, a triad of unrelated persons is formed and in the second, a triad of related persons is formed.
- Alan D'Souza, iamaland@gmail.com
 
(The other problem was: "Fill in the blank with the suitable number in words: 'This sentence has . letters'- MS)
 
Let-Us-In-Words Dept:
Here is the answer: The word to be filled in the blank is THIRTY ONE. Counting the number of words in the complete sentence, the number of words in the sentence is 31. So the new sentence is: "This sentence has THIRTY ONE letters".
- Jaelyne Tauro, jaelynetauro@gmail.com
 
"This sentence has THIRTY THREE letters".
- Siddharth Patkar, siddhpatkar@gmail.com
 
(Among the first five to also get it right are: Vivian Joseph, vivianjoseph@mail.com; Madihah Anaum, safirdose@gmail.com; Priyanka Awatramani, priyankag1010@gmail.com; Niraj Nandish, nirajnandish@icloud.com; Arya Manoj, arulachu02@gmail.com.)
 
(The third one was: "A cell phone is bought and you start adding names and install apps. Does the weight of the phone increase?" - MS)
 
Weight's-App-Doc? Dept:
The weight of the phone actually increases. This was proven by U C Berkeley professor John D Kubiatowicz. The extra weight comes from flash storage storing more data in memory. The transistors distinguish between a 1 and a 0 by trapping electrons. The more data it stores, the more electrons are trapped. And these do have weight: For 4GB of data, the difference between full and empty is 10^-18 grams. For 64GB data, it would be 12 times that. Also, a smartphone with a dead battery has less weight than one with a full battery.
- Akshit Chaturvedi, akshit0201@gmail.com
 
ENDGAMES
 1. 'N' people each know a different piece of gossip. They can telephone each other and exchange all the information they know (so that after the call they all know something that either of them knew before the call). What is the smallest number of calls needed so that everyone knows everything?
2. TWO*SIX = TWELVE. Find the digits that the letters represent and thus the three numbers that are represented by TWO, SIX and TWELVE such that they also satisfy the equation TWO*SIX = TWELVE.

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

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