Brain Teasers
Question Mark's Function Machine MKIII
Question Mark cannot get enough of changing the formula to his function machine. This time, one number goes in, but TWO numbers come out. If:
9 -> 576 & 72
10 -> 810 & 90
11 -> 1100 & 110
12 -> 1452 & 132
13 -> 1872 & 156
What will come out if 25 goes in?
9 -> 576 & 72
10 -> 810 & 90
11 -> 1100 & 110
12 -> 1452 & 132
13 -> 1872 & 156
What will come out if 25 goes in?
Answer
14400 & 600. The formula is n^3 - n^2. The numbers are then split by the formula of (n-1)/n & 1/n. In other words:9^3 (729) - 9^2 (81) = 648
>8/9*648 = 576, 1/9*648 = 72
10^3 (1000) - 10^2 (100) = 900
>9/10*900 = 810, 1/10*900 = 90
11^3 (1331) - 11^2 (121) = 1210
>10/11*1210 = 1100, 1/11*1210 = 110
12^3 (1728) - 12^2 (144) = 1584
>11/12*1584 = 1452, 1/12*1584 = 132
13^3 (2197) - 13^2 (169) = 2028
>12/13*2028 = 1872, 1/13*2028 = 156
And therefore:
25^3 (15625) - 25^2 (625) = 15000
>24/25*15000 = 14400, 1/25*15000 = 600
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Comments
another easy one..
? after seeing the answer of the first one, I've got the idea.
More coming?
More coming?
Once again that was insanely easy.... u really need to give up off this teaser.. it is way too easy
Yes, I will probably write more .
I find it easier to come up with the factors: n(n-1)^2 and n(n-1)
Timed myself at just under 12 seconds to do it. Though rather than get the formula i done a different way. Though if i put my way into an equation, it will probably get your formula but too early in morning for that. I just done, ((n - 1)^2)n to give the first number. An the second number was just n^2 - n
Yep, simplifying the answer does give my way...
Apr 13, 2006
I have to make mention that your third function machine is not a function by definition at all...it is a combination of functions. If an equation produces two outputs from one input it isn't a function. You should let people know when they are doing the puzzle that there are multiple functions at work.
Follows similar logic as the earlier two puzzles. Quite easy.
OK, the first one was kinda fun, the second not quite as fun and now they're just boring.
First attempt was the correct equation for each of the problems. Combined time to deteremine the equations, verify the equations and compute the answer for all three of these teasers is under a minute. The smallest part of that time was spent determining the function and the largest part spent verifying the function.
First attempt was the correct equation for each of the problems. Combined time to deteremine the equations, verify the equations and compute the answer for all three of these teasers is under a minute. The smallest part of that time was spent determining the function and the largest part spent verifying the function.
Interesting how math works, because there's an alternate way that works too. Can also do:
n*(n-1)^2 for the first number. Then n*(n-1) for the 2nd number.
I.E., for 25:
25*(25-1)^2
=25*24^2
=25*576
=14,400
And
25*24 = 600
n*(n-1)^2 for the first number. Then n*(n-1) for the 2nd number.
I.E., for 25:
25*(25-1)^2
=25*24^2
=25*576
=14,400
And
25*24 = 600
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