Brain Teasers
Question Mark's Function Machine
Question Mark is very proud with himself. He has just designed his very own function machine. When a number goes into this machine, a different number comes out. A basic formula is used to determine what comes out. If:
3 -> 90
4 -> 272
5 -> 650
6 -> 1332
7 -> 2450
What will come out if 10 goes in?
3 -> 90
4 -> 272
5 -> 650
6 -> 1332
7 -> 2450
What will come out if 10 goes in?
Answer
10100. The formula is n^4 + n^2. In other words:3^4 (81) + 3^2 (9) = 90
4^4 (256) + 4^2 (16) = 272
5^4 (625) + 5^2 (25) = 650
6^4 (1296) + 6^2 (36) = 1332
7^4 (2401) + 7^2 (49) = 2450
And therefore:
10^4 (10000) + 10^2 (100) = 10100
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Comments
Got me! Very suave...
? was this part of your homework?
sort of easy, using some combination of indices to inflate numbers
Been a long time since I used formulas. Thought I had it figured out but I was wrong. Good Job.
I find it easier to come up with the factors: n^2(n^2+1)
I got it. But I took the long route.
3 -> 90/3->30/3=10
4 -> 272//4->68/4=17
5 -> 650/5->130/5=26
6 -> 1332/6->222/6=37
7 -> 2450/7->350/7=50
10->x->y=101
You will get 101 if you follow this pattern:
10+7 =17
17+9=26
26+11=37
37+13=50
50+15=65
65+17=82
82+19=101
From the above equation, we get
10y=x
y/10=101
y=1010
x=10100
I know, it's a lenghty solution, but I got it right
3 -> 90/3->30/3=10
4 -> 272//4->68/4=17
5 -> 650/5->130/5=26
6 -> 1332/6->222/6=37
7 -> 2450/7->350/7=50
10->x->y=101
You will get 101 if you follow this pattern:
10+7 =17
17+9=26
26+11=37
37+13=50
50+15=65
65+17=82
82+19=101
From the above equation, we get
10y=x
y/10=101
y=1010
x=10100
I know, it's a lenghty solution, but I got it right
Got the answer with the same formula as used by Sahana!
Lucky guess probably, but that was the first thing I tried.
Based on the rate of increase, I was pretty sure it was a fourth-order equation, so I tried the simplest fourth-order equation that solved for 3 and 90 and it was the right one.
Based on the rate of increase, I was pretty sure it was a fourth-order equation, so I tried the simplest fourth-order equation that solved for 3 and 90 and it was the right one.
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