3 ms·

Can you give an example? I am intrigued, although suspect you are making a joke!

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jacobwilliamroy 6y ago
You can check the properties of digital roots on wikipedia: https://en.wikipedia.org/wiki/Digital_root#Properties https://en.wikipedia.org/wiki/Digital_root#Properties Example from ASVAB practice math test: (x+4)(x+4) = A. x^2+16x+8 B. x^2+16x+16 C. x^2+8x+16 D. x^2+8x+8 Since we don't have to solve for X in this problem, we can just assume x is 1, which would make the digital root of the problem expression 7. Assuming x = 1, the digital roots of A, B, C and D are 7, 6, 7 and 8 respectively. C is the answer because its last term is the square of 4.
- flir 6y ago
  I can't decide if I've just seen magic, or conjuring. I'm gonna have to go away and think about this.
- plutonorm 6y ago
  Perhaps I am being dumb, but I don't see what the digital root brings to this. You can do the same thing without the digital root. substitute 1 into all the possible answers gives: A: 25 B: 33 C: 25 D: 17 Substitute 1 into the question gives 25. Therefore only A and C are possible answers and it must be C because 4*4 = 16 This is the same process as your answer but without the digital root!
  - callmekit 6y ago
    Maybe is case of large numbers you can compute digital root easier than the answer. For example, 25 * 26 = 650, digital root 2. Or take digital root of 25 and 26 first, get 7 * 8 = 56, same digital root 2.
  - jacobwilliamroy 6y ago
    I suppose such is possible without digital roots. Let's try the same problem, but this time we'll multiply our constants by 3,571: (x + 14284) (x + 14284)= A: x^2 + 204032656x + 28568 B: x^2 + 204032656x + 204032656 C: x^2 + 28568x + 204032656 D: x^2 + 204032656x + 204032656 The digital root of the problem expression is 4. The digital roots of A, B, C and D are 4, 6, 4 and 3 respectively. The digital root of the square of 14284 is 1, and the digital roots of the last term of A and C are 2 and 1, respectively. The answer is C.
    - dragonwriter 6y ago
      Of course, it is quicker just to multiply and add the last digit of the constant to find the only possible answer (or count digits to get an order of magnitude estimate, which will also show C as the only possible answer). When a problem of this form uses big enough numbers to warrant a shortcut, digital root is almost always a suboptimal shortcut.
      - jacobwilliamroy 6y ago
        Yes you are the heuristics master!
  - taneq 6y ago
    Agreed. The real trick here is knowing that, since we don't need to find x, we can sub in an arbitrary x and do the comparison numerically instead of algebraically. Of course there's a tiny chance that one of the other equations would be equal at your arbitrary x value. If so and you get two 'right' answers just try again with a different x.
    - benibela 6y ago
      It is the DeMillo-Lipton-Schwartz–Zippel lemma If two polynomials evaluate to equal numbers with random variables values, the polynomials are almost certainly equal themselves Ofc, x = 0 and x = 1 are hardly random
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You can check the properties of digital roots on wikipedia: https://en.wikipedia.org/wiki/Digital_root#Properties https://en.wikipedia.org/wiki/Digital_root#Properties Example from ASVAB practice math test: (x+4)(x+4) = A. x^2+16x+8 B. x^2+16x+16 C. x^2+8x+16 D. x^2+8x+8 Since we don't have to solve for X in this problem, we can just assume x is 1, which would make the digital root of the problem expression 7. Assuming x = 1, the digital roots of A, B, C and D are 7, 6, 7 and 8 respectively. C is the answer because its last term is the square of 4.

flir 6y ago
I can't decide if I've just seen magic, or conjuring. I'm gonna have to go away and think about this.
plutonorm 6y ago
Perhaps I am being dumb, but I don't see what the digital root brings to this. You can do the same thing without the digital root. substitute 1 into all the possible answers gives: A: 25 B: 33 C: 25 D: 17 Substitute 1 into the question gives 25. Therefore only A and C are possible answers and it must be C because 4*4 = 16 This is the same process as your answer but without the digital root!
- callmekit 6y ago
  Maybe is case of large numbers you can compute digital root easier than the answer. For example, 25 * 26 = 650, digital root 2. Or take digital root of 25 and 26 first, get 7 * 8 = 56, same digital root 2.
- jacobwilliamroy 6y ago
  I suppose such is possible without digital roots. Let's try the same problem, but this time we'll multiply our constants by 3,571: (x + 14284) (x + 14284)= A: x^2 + 204032656x + 28568 B: x^2 + 204032656x + 204032656 C: x^2 + 28568x + 204032656 D: x^2 + 204032656x + 204032656 The digital root of the problem expression is 4. The digital roots of A, B, C and D are 4, 6, 4 and 3 respectively. The digital root of the square of 14284 is 1, and the digital roots of the last term of A and C are 2 and 1, respectively. The answer is C.
  - dragonwriter 6y ago
    Of course, it is quicker just to multiply and add the last digit of the constant to find the only possible answer (or count digits to get an order of magnitude estimate, which will also show C as the only possible answer). When a problem of this form uses big enough numbers to warrant a shortcut, digital root is almost always a suboptimal shortcut.
    - jacobwilliamroy 6y ago
      Yes you are the heuristics master!
- taneq 6y ago
  Agreed. The real trick here is knowing that, since we don't need to find x, we can sub in an arbitrary x and do the comparison numerically instead of algebraically. Of course there's a tiny chance that one of the other equations would be equal at your arbitrary x value. If so and you get two 'right' answers just try again with a different x.
  - benibela 6y ago
    It is the DeMillo-Lipton-Schwartz–Zippel lemma If two polynomials evaluate to equal numbers with random variables values, the polynomials are almost certainly equal themselves Ofc, x = 0 and x = 1 are hardly random
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