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Given:

SIX + ZERO = 4

TWO + THREE = 15

FIVE + SIX = 88

ONE + TWO = 83

TEN + TWO = 13

If so, is TWO + TWO = 2 correct?

What is TEN + TEN ? NINE + NINE ?

Hint 1

NINE + TWO= 23 TEN - TWO = 11

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  • $\begingroup$ Based on well known system..since nobody got it so far, I am going to add couple of equations in the hint. Which will lead to easy solution $\endgroup$ – Uvc Jun 8 at 18:52
  • $\begingroup$ "easy solution" not necessarily. Sometimes the solution to the puzzle seems easier to the OP than it might be in reality. $\endgroup$ – Brandon_J Jun 9 at 1:15
  • $\begingroup$ True..because of more familiarity..in this case I meant relative to before the hint.. $\endgroup$ – Uvc Jun 9 at 1:53
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My attempts:

I thought that SIX + ZERO = 4 $\implies$ S + I + X + Z + E + R + O = 4 ...(i)

Similarly, 2T + 2E + W + O + H + R = 15 ...(ii)

F + 2I + V + E + S + X = 88 ...(iii)

2O + N + E + T + W = 83 ...(iv)

2T + N + E + O + W = 13 ...(v)

From (iv) and (v),

O - T = 70 ...(vi) I found some more equations like above. But the hints made it even simple.

From the hints,

TEN - TWO = 11 also we have TEN + TWO = 13
On adding, 2(TEN) = 2(T+E+N) = 24 or TEN = 12
$$TEN+ TEN= 24$$
On Subtracting, 2(TWO) = 2
TWO + TWO = 2 True (asked in the question)
So, TWO = 1
As, NINE + TWO = 23 $\implies$ NINE = 23 -1 = 22
$$NINE + NINE = 22 +22 = 44$$

Verification

TEN + TWO = 13, we have TEN = 12, TWO = 1, so it holds.
ONE + TWO = 83
On subtracting, ONE = 83 - 1 = 82
Working on other equations...

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  • $\begingroup$ nice answer! @Ak19 $\endgroup$ – Omega Krypton Jun 9 at 13:39
  • $\begingroup$ Thank you @OmegaKrypton $\endgroup$ – Ak19 Jun 9 at 13:39
  • $\begingroup$ Is it solvable without the hints a.k.a there may be more than one solutions? $\endgroup$ – athin Jun 11 at 6:49
  • $\begingroup$ @ athin I don't know, first I tried before the hint was posted, didn't get the solution and left it. The day before yesterday, I saw the hint and tried, it worked :) $\endgroup$ – Ak19 Jun 11 at 7:17
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From the hint, since we have

$$\mathrm{TEN} + \mathrm{TWO} = 13$$

and

$$\mathrm{TEN} - \mathrm{TWO} = 11$$

then it follows that

$\mathrm{TWO} = 1$, and $\mathrm{TEN} = 12$.

Hence both

TWO + TWO = 2 and TEN + TEN = 24.

Now since

$$\mathrm{NINE} + \mathrm{TWO} = 23$$

and we already know

$\mathrm{TWO}$,

we have

$\mathrm{NINE} = 22$.

Hence

NINE + NINE = 44.

All the other equations are superfluous.

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