Hi all , I figure this is an inteersting (yet weird in my opinion) question: Ralph likes 25 however not 24; he likes 400 however not 300; he likes 144 but not 145. Which does he like: a)10 b)50 c)124 d)200 e)1600 Any concepts ?

You are watching: Ralph likes 25 but not 24; he likes 400 but not 300; he likes 144 but not 145. which does he like:

posted 9 years ago

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posted 9 years ago

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Ryan, much like Ralph, likes 25 yet not 24, and he likes 144 yet not 145. However before, unlike his friend Ralph, Ryan likes 300 but not 400. Which one (and just one) of the adhering to does he like? a) 37 b) 64 c) 200 d) 1024 e) 65535 (...and why?)
This reasoning might be non feeling . also though would certainly choose to give a try : below is my Observation : Lets take into consideration 1 to 10* Ralphs like: 25 => 2+5 = 7 odd number 144 => 1+4+4 = 9 odd number 300 => 3+0+0 = 3 odd number Ralph"s dislike: 24 => 2+4 = 6 even 145 = > 1+4+5 = 10 even 400 => 4+0+0 = 4 even Options: 37 => 3+7 = 10 also 64 => 6+4 = 10 even 200 => 2+0+0 = 2 also 1024 => 1+0+2+4 = 7 odd 65535 => 6+5+5+3+5 => 11+8+5 => 19+5 => 2+4 => 6 also So my guess would be 1024 .
Given the indevelopment presented so far, that seems favor a perfectly reasonable explacountry, Seetharamale. You also came up through the correct answer (wright here "correct" is defined as "what I was thinking"), but for a different factor. We currently understand that 25, 144, 300 and 1024 are "likable" but 24, 145, 400, 37, 64, 200 and 65535 are "unlikable". However before, I"m going to declare that 8889 is likable while 97 unlikable. How deserve to that perhaps be?
My take is that Ryan likes numbers wright here the distinction of amount of the alternate digits is odd. Here is my logic - Ryan"s likes: 25 => 5 – 2 = 3Odd 144 => (1+4) – 4 = 1Odd 300 => (3+0) – 0 = 3Odd Ryan"s dislikes: 24 => 4 – 2 = 2Even 145 => (1+5) – 4 = 2Even 400 => (4+0) – 0 = 4Even Also, as currently declared, 8889 => (8+9) – (8+8) = 1Odd 97 => 9 -7 = 2Even So offered all the over, the available options are: 37 => 7 – 3 = 4Even 64 => 6 – 4 = 2Even 200 => (2+0) – 0 = 2Even 1024 => (4+0) – (1+2) = 1Odd 65535 => (6+5+5) – (3+5) = 8Even That leaves 1024 as the only alternative

Anubrato Roy wrote:My take is that Ryan likes numbers wright here the distinction of sum of the different digits is odd.

I would say that qualifies as "humorously correct". Yes, I perform indeed favor 1024. Also, the rule you declared will certainly correctly identify numbers I favor versus the ones I don"t choose. However before, the statement of the ascendancy is even more facility than the one I had in mind. If we recognize that the distinction between two numbers is either even or odd, what can we say around the sum of those exact same numbers? If 2 numbers have actually an even amount, just how even numbers did we start with? How many odd? (Addition is associative and also commutative.) Is tbelow a less complicated ascendancy that is equivalent to the "odd difference of sums of alternative digits" one offered above?
Hi Ryan, It was amusing to realize that I have actually declared the preeminence in a complex manner. Taking your hint, if the distinction of 2 numbers is odd, then one of them is even and also the other odd - which suggests that their sum is also odd. That combined via my logic sindicate implies that the sum of all the digits in the number should be odd. So below is the revised version - You prefer numbers wbelow the amount of digits of the numbers is Odd
. That provides me realize that this is virtually identical to Seetharaman"s logic, except that I stop only at the first pass of summing up the digits; and also not summing up the digits of the sum itself. Regards, Anubrato

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Anubrato Roy wrote: So below is the revised version - You like numbers wright here the sum of digits of the numbers is Odd.

As it transforms out, that"s correct and also now being relatively succinct. What I really favor about the "likable" numbers is that they have actually an odd number of odd digits. ...which turns out to be indistinguishable to liking numbers where the amount of digits is odd.