# Is it True that Two + Two = 2? If so, what is Ten + Ten and Nine + Nine?

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

• 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 – Uvc Jun 8 '19 at 18:52
• "easy solution" not necessarily. Sometimes the solution to the puzzle seems easier to the OP than it might be in reality. – Brandon_J Jun 9 '19 at 1:15
• True..because of more familiarity..in this case I meant relative to before the hint.. – Uvc Jun 9 '19 at 1:53

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...

• nice answer! @Ak19 – Omega Krypton Jun 9 '19 at 13:39
• Thank you @OmegaKrypton – Ak. Jun 9 '19 at 13:39
• Is it solvable without the hints a.k.a there may be more than one solutions? – athin Jun 11 '19 at 6:49
• @ 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 :) – Ak. Jun 11 '19 at 7:17

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

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

$$\mathrm{TWO}$$,
$$\mathrm{NINE} = 22$$.