Toughest Brain Twister Question - 14 November
2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
Solve it ?
Solution
Fastest (Amit Singh)
By Tomasz Budzeń (Best Explained)
n A B C=A-B C(n) - C(n-1) = 2
0 2
1 2 + 3 = 8 2*3 = 6 2 4
2 3 + 7 = 27 3*7 = 21 6 6
3 4 + 5 = 32 4*5 = 20 12 8
4 5 + 8 = 60 5*8 = 40 20 10
5 6 + 7 = 72 6*7 = 42 30 12
6 7 + 8 = ?? 7*8 = 56 (42)
(Pascal's difference machine)
A(n) =
B(n) + C(n) = a(n) * b(n) + C(n) = a(n) * b(n) + (n-1) * (n-2) = (n+1) * b(n) + n * (n+1)
So:
A(n) = (n + 1) * (b(n) + n) [it doesn't depend on a]
And:
A(6) = 7 * (8 + 6) = 7 * 14 = 98
2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
Solve it ?
Solution
Fastest (Amit Singh)
By Tomasz Budzeń (Best Explained)
n A B C=A-B C(n) - C(n-1) = 2
0 2
1 2 + 3 = 8 2*3 = 6 2 4
2 3 + 7 = 27 3*7 = 21 6 6
3 4 + 5 = 32 4*5 = 20 12 8
4 5 + 8 = 60 5*8 = 40 20 10
5 6 + 7 = 72 6*7 = 42 30 12
6 7 + 8 = ?? 7*8 = 56 (42)
(Pascal's difference machine)
A(n) =
B(n) + C(n) = a(n) * b(n) + C(n) = a(n) * b(n) + (n-1) * (n-2) = (n+1) * b(n) + n * (n+1)
So:
A(n) = (n + 1) * (b(n) + n) [it doesn't depend on a]
And:
A(6) = 7 * (8 + 6) = 7 * 14 = 98
