Some Daffy Notions

The first letter of each word is different except for the X, Y and Z, which have been lumped together as one

E4
Here's a classic definitions problem from over a decade ago that generated a lot of controversy, which is the main reason we're running it again. It's difficult, but one hint is that the first letter of each word is different except for the X, Y and Z, which have been lumped together as one (therefore 24 and not 26). So if you have two words beginning with A or M or U, then one of them has to be wrong. Also, in one case, an American spelling has been used. If you get five right consider yourself a puss in collar-high boots. Ten and above, zip it over your head.
(1)   Bashful or shy; (2) going down or a military retreat; (3) having all four feet adapted for use as hands; (4) to make a nest; (5) the eating of dry food, especially as a form of fast; (6) of or like an angel; (7) to stride along exultantly; (8) slow in perceiving; (9) full of freckles; (10) loud and grossly abusive; (11) tightrope walker; (12) a teller of untruths; (13) without shoes; (14) of or pertaining to dreams; (15) small artistic object of beauty or rarity; (16) apparition, phantom or ghost; (17) having horns or horn-like projections; (18) to make or become thick or thicker; (19) having woolly or crisply curly hair; (20) to spend the summer; (21) to check or suppress by extreme measures; (22) flowering more than once in a season; (23) having large ears; (24) use of words superfluously or redundant.
DEAR MS
(One problem that needs to be re-addressed is with reference to the smallest integer consisting only of and divisible by 3, 5 and 7 with sum of the digits also divisible by 3, 5 and 7. - MS)
Numbering-Bias Dept:
My analysed solution concluded the smallest number as 33,577,577,777,777,775, which is lower than the number given by you. You are fortunate in not being before the king who asked this question.
Abhay Prakash, ?abhayprakash@hotmail.com
(The older problem was: "A and B are given one each of two consecutive natural numbers n and n + 1. Both know that the numbers are consecutive, although neither knows whose number is bigger. After every minute, a beep is heard and each is asked to say out aloud whether she knows the other's number. Who is the first person to guess correctly and after how many beeps?" - MS)
For-The-Nth-Time Dept:
The girl who gets n (ie, the smaller number) will be the first one to guess correctly after n beeps. Here's how. Let's start with n = 1. In this case, the person getting a 1 guesses instantaneously and produces the answer at the first beep. For n = 2, the person has to wait till the first beep to know whether the other person can conclude about herself (ie, if she has got 1); she then comes up with the answer in the second beep. And so on. Proceeding by mathematical induction, the person who is given n will guess correctly after n beeps.

• Dhruv Narayan, dhruv510@gmail.com

(The other problem was regarding the 10 prisoners with black or white hats who had to devise a method to save their necks. - MS)
Captive-Audience-Dept:
The prisoners make a plan that if the 10^th prisoner sees an odd number of black hats, he will say black. This way the nine other prisoners will know their own hat colour after the prisoner behind him responds. Also, this way at least nine prisoners will survive and the 10^th one has a 50 per cent chance for survival. Vinod Mahajan, vm1966@gmail.com
ENDGAME(S)

1. How will an astronaut use a pan balance to weigh 5kg while in a rocket travelling in space with no gravity? Will the scales tilt towards the heavier end in space too?

- (Submitted by Krishna, ?krishp84@gmail.com)  

2. A store prices its items at US$4, $0.50 and $0.25. A person purchases 20 items for a total of $20. How many items of each does he buy?

- (Submitted by Sheikh Sintha Mathar, sheikhsm7@gmail.com)
(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)
 
 

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