## Recommended Posts

If letters are factors of equations:
zero = 0
one = 1
two = 2
three = 3
four = 4
five = 5
six = 6
seven = 7
eight = 8
nine = 9
ten = 10
twelve = 12
fifteen = 15
twenty = 20
thirty = 30
forty = 40
sixty = 60
hundred = 100
thousand = 1000
million = 1000000
billion = 1000000000

What is the product for unanswered = ?

##### Share on other sites

If letters are factors of equations:

zero = 0

one = 1

two = 2

three = 3

four = 4

five = 5

six = 6

seven = 7

eight = 8

nine = 9

ten = 10

twelve = 12

fifteen = 15

twenty = 20

thirty = 30

forty = 40

sixty = 60

hundred = 100

thousand = 1000

million = 1000000

billion = 1000000000

What is the product for unanswered = ?

By looking at this "impossible" puzzle, I shall answer it to the best of my ability.

Z.E.R.O = 0 Therefore those letters are worth zero.

O.N.E = 1, since we know that O. and E. = 0, then N = 1.

T.W.O = 2 we know that O = 0, so the letters T. and W. > 0

T.H.R.E.E = 3

F.O.U.R = 4

F.I.V.E = 5

S.I.X = 6

S.E.V.E.N = 7

E.I.G.H.T = 8

N.I.N.E = 9 Since we know that E = 0 and that N = 1, we know that I = 7

T.E.N =10 since we know E = 0 and that N = 1, we know that T = 9

Someone else finish it, I ain't got the time.

##### Share on other sites

By looking at this "impossible" puzzle, I shall answer it to the best of my ability.

Z.E.R.O = 0 Therefore those letters are worth zero.

O.N.E = 1, since we know that O. and E. = 0, then N = 1.

T.W.O = 2 we know that O = 0, so the letters T. and W. > 0

T.H.R.E.E = 3

F.O.U.R = 4

F.I.V.E = 5

S.I.X = 6

S.E.V.E.N = 7

E.I.G.H.T = 8

N.I.N.E = 9 Since we know that E = 0 and that N = 1, we know that I = 7

T.E.N =10 since we know E = 0 and that N = 1, we know that T = 9

Someone else finish it, I ain't got the time.

##### Share on other sites

@Raider-

if (z)(e)(r )(o)=0 maybe not "all" of those factors are equal to zero.

one= o X n X e

Edited by TimeSpaceLightForce

##### Share on other sites

@Raider-

if (z)(e)(r )(o)=0 maybe not "all" of those factors are equal to zero.

one= o X n X e

In the sense it is an impossible puzzle.

##### Share on other sites

Sur

If letters are factors of equations:
zero = 0
one = 1
two = 2
three = 3
four = 4
five = 5
six = 6
seven = 7
eight = 8
nine = 9
ten = 10
twelve = 12
fifteen = 15
twenty = 20
thirty = 30
forty = 40
sixty = 60
hundred = 100
thousand = 1000
million = 1000000
billion = 1000000000

What is the product for unanswered = ?

one = 1

ten = 10

two = 2

I read this in terms of puzzle as

o * n * e = 1

t * e * n =10

and

t*w*o =2

If so then (unless so of the letters are fractions - which would be silly)

o =1 and n=1 and e=1 - if any of them are not unity then the product would not be one

this gives the second line reading

t*1*1=10

t=10

which is pretty annoying as ten is not a prime factor (but you didn't say prime factors)

but this then gives

10*w*1=2

w cannot be an integer (it is 1/5)

You get the same internal contradiction with nine - i must equal 9 but that screws up six

##### Share on other sites

@imatfaal-why should the factors(letters) be all whole numbers?

##### Share on other sites

@imatfaal-why should the factors(letters) be all whole numbers?

Because that is the common use of the term

http://mathworld.wolfram.com/Factor.html

##### Share on other sites

There's only two solutions for most of the letters (m, b, and I think l are ambiguous, but unnecessary). Some of these could be negative instead; I haven't checked to see whether that changes the answer, but I doubt it.

Use the fact that sixty = 60 = 6*10 = six*10 to deduce that ty = 10. Then use the fact that forty = 40 = 4*10 = four*10, so u = 1.

u = 1

w = 1/5 using twenty = 20, ty = 10, ten = 10.

t = 10 using ten = 10, two = 2, and one = 1.

y = 1 using ty = 10.

o = 1 using two = 2.

From thirty = 30 = three*10, deduce that i = ee. Then:

e = 9 using one = 1, nine = 9, and i = ee.

n = 1/9 using one = 1.

i = 81 using nine = 9.

f = sqrt(1/486) using fifteen = 15.

v = 5 sqrt(6)/81 using five = 5.

s = 21 sqrt(6)/10 using seven = 7.

r = 36 sqrt(6) using four = 4.

h = sqrt(6)/58320 using three = 3

d = sqrt(27000) using hundred = 100

a = 32400 sqrt(30)/7 using thousand = 1000

Unanswered = 1*1/9*32400 sqrt(30)/7*1/9*21 sqrt(6)/10 * 1/5 * 9 * 36 sqrt(6) * 9 * sqrt(27000) = 377913600.

I've probably made some arithmetic error somewhere, but the order should work.

Edited by uncool

##### Share on other sites

@imatfaal- thanks for clarifying that factors are Integers..I took the wrong term and it should be " If letters are values to multiply in equations:" so on..

@Raider5678-I see now why you think it is impossible. Because factors are not fractions.

There's only two solutions for most of the letters (m, b, and I think l are ambiguous, but unnecessary). Some of these could be negative instead; I haven't checked to see whether that changes the answer, but I doubt it.

Use the fact that sixty = 60 = 6*10 = six*10 to deduce that ty = 10. Then use the fact that forty = 40 = 4*10 = four*10, so u = 1.

u = 1

w = 1/5 using twenty = 20, ty = 10, ten = 10.

t = 10 using ten = 10, two = 2, and one = 1.

y = 1 using ty = 10.

o = 1 using two = 2.

From thirty = 30 = three*10, deduce that i = ee. Then:

e = 9 using one = 1, nine = 9, and i = ee.

n = 1/9 using one = 1.

i = 81 using nine = 9.

f = sqrt(1/486) using fifteen = 15.

v = 5 sqrt(6)/81 using five = 5.

s = 21 sqrt(6)/10 using seven = 7.

r = 36 sqrt(6) using four = 4.

h = sqrt(6)/58320 using three = 3

d = sqrt(27000) using hundred = 100

a = 32400 sqrt(30)/7 using thousand = 1000

Unanswered = 1*1/9*32400 sqrt(30)/7*1/9*21 sqrt(6)/10 * 1/5 * 9 * 36 sqrt(6) * 9 * sqrt(27000) = 377913600.

I've probably made some arithmetic error somewhere, but the order should work.

All the letter values are correct! You'll just get it answered.. (the error is somewhere in the multiplication for the product)

##### Share on other sites

Nice one uncool. I was attempting to do it without any recourse to numbers whatsoever - I got close but then time constraints stopped me

To explain - If I want UNANSWERED then I can build it from other words

ie SIX/SIXTY = 1/TY

SIX/SIXTY * FORTY = FOR

SIX/SIXTY*FORTY/FOUR = 1/U

etc

THOUSAND * TWENTY * SIX/SIXTY = THOUSANDTWEN

THOUSANDTWEN/TEN = THOUSANDW = UNA_SW___D THO

UNA_SW___D THO / TWO = UNA_SW___D / W

UNA_SW___D / W * THREE = UNA_SWERED.TH/W

UNA_SWERED.TH/W * TEN/TWENTY * SIXTY/SIX = UNA_SWERED.TH

...

##### Share on other sites

imatfaal: it's possible to do exactly that as a linear algebra problem. Each letter gives a component of a vector; a word is then a vector in the space of letter-products. Multiplying two words is adding two vectors. We're then looking for the vector 1u + 2n + 1a + 1s + 1w + 2e + 1r + 1d in terms of the rest. I think in the end, there's a coefficient of 1/2, which is why there will be sign ambiguity. Edit: it turns out there isn't any; all the "halves" do cancel out, so there is no ambiguity in the answer.

Start by identifying letters that only appear in a few places. Here, 'a' only appears in 'thousand, so to get unanswered, you need thousand.

Using 'h', and keeping bookkeeping neat with 'two': nwere/tho = 1/twothree * nweretwothree/tho = 1/6 * nwerewtree

Rearranging: nwweeeerrt

Using 'r': nwweeeerrt = fortyforty*nwweeeerrt/fortyforty = 1600*nwweeeet/fotyfoty

Using 'f': nwweeeet/fotyfoty = 1/fifteen*nwweeeetfifteen/fotyfoty = 1/15 * nnwweeeeeei/ooyy

The problem is harder from here on out.

w = twenty six/ten sixty

to = two ten sixty/twenty six

oo = two sixty one/twenty six

nene = twenty six one/two sixty

neene = nine three sixty/thirty six

e = two three nine sixty sixty/one six six twenty thirty

i = two two three nine nine sixty sixty sixty/one one six six six twenty twenty thirty

tt = tenten/nene = ten ten two sixty/twenty six one

yy = tyty/tt = sixty twenty one/six ten ten two

nnwweeeeeei/ooyy = nine*wweeeee/ooyy = two^5 three^5 nine^6 sixty^6/one^7 six^6 twenty^3 thirty^5

Using earlier calculations: unanswered = two^4 three^4 nine^6 forty^2 sixty^6 thousand/one^7 six^6 fifteen twenty^3 thirty^5

Also, how did you come up with this problem?

Edited by uncool

##### Share on other sites

@uncool- I thought it was 340122240 which is I just remembered is the product computed for "answered" .

Since un=1/9 , 37791360 really answers this problem. Note that I have posted this in this section 4 years ago

-It started with the anagram "one+twelve=two+eleven" ..as I could remember.

##### Share on other sites

If letters are factors of equations:

zero = 0

one = 1

two = 2

three = 3

four = 4

five = 5

six = 6

seven = 7

eight = 8

nine = 9

ten = 10

twelve = 12

fifteen = 15

twenty = 20

thirty = 30

forty = 40

sixty = 60

hundred = 100

thousand = 1000

million = 1000000

billion = 1000000000

What is the product for unanswered = ?

The product of anything multiplied by zero is zero.