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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