# Letter Problems

phgao
Posers and Puzzles 21 Jul '05 11:32
1. 21 Jul '05 11:321 edit
1. Adab + Cbb + Caa = Abda
2. Abab - Ccd = Bac
3. Abab - Ccba = Ccdc
4. Efg + Gf + Gef = Bdfg
5. Abcb - Deac = Eadd

Note that A = a, B = b et cetera.

Edit: corrected problem
2. 21 Jul '05 12:011 edit
Originally posted by phgao
1. Adab + Cbb + Caa = Abda
2. Abab - Cdd = Bac
3. Abab - Ccba = Ccdc
4. Efg + Gf + Gef = Bdfg
5. Abcb - Deac = Eadd

Note that A = a, B = b et cetera.
uhm... maybe I made a mistake:

1. 1021A+12B+200C+100D = 1001A+100B+10D
20A+200C+90D=88B
2. 1010A +101B - 100C - 11D = 100B + 10A + C
1000A + B = 101C + 11D
3. 1010A + 101B – 1100C – 10B - A = 1101C + 10D
1009A + 91B = 2201C + 10D
4. 110E + 12F + 111G = 100B + 100D + 10F + G
110E + 2F + 110G = 100B + 100D
5. 1000A + 101B + 10C - 1000D – 100E – 10A - C = 1000E + 100A + 11D
890A + 101B + 9C = 1100E + 1011D

10A + 100C + 45D = 44B
1000A + B = 101C + 11D
1009A + 91B = 2201C + 10D
55E + F + 55G = 50B + 50D
890A + 101B + 9C = 1100E + 1011D

the only possible numbers in the first one are:
A = 3
B = 5
C = 1
D = 2

then you get:
30+100+90=220
220=220 (i'm a genius ðŸ˜›)

but if you look at the second:
3000 + 5 = 101 + 22
3005 = 123 uhm... I don't think that's correct...

so, are you really sure you didn't wrote a letter wrong?
3. 21 Jul '05 12:242 edits
Originally posted by Florrat
uhm... maybe I made a mistake:

1. 1021A+12B+200C+100D = 1001A+100B+10D
20A+200C+90D=88B
2. 1010A +101B - 100C - 11D = 100B + 10A + C
1000A + B = 101C + 11D
3. 1010A + 101B – 1100C – 10B - A = 1101C + 10D
1009A + 91B = 2201C + 1 ...[text shortened]... ct...

so, are you really sure you didn't wrote a letter wrong?
Oh sorry for the second one it should be Abab - ccd = bac

But the 1st one is correct. Each one has a separate solution. So the A for Q1 doesnt have to be the same a in Q2 etc.
4. 21 Jul '05 16:061 edit
Originally posted by phgao
Oh sorry for the second one it should be Abab - ccd = bac

But the 1st one is correct. Each one has a separate solution. So the A for Q1 doesnt have to be the same a in Q2 etc.
these are the solutions (2 and 4 have multiple answers...):

1. 10A + 100C + 45D = 44B A = 3, B = 5, C = 1, D = 2
2. 1000A + B = 111C + D A = 1, B = 2~7 = D-1, C = 9, D = 3~8 = B+1 (6 possible solutions)
3. 1009A + 91B = 2201C + 10D A = 2, B = 3, C = 1, D = 9
4. 55E + F + 55G = 50B + 50D B = (1~)2, D = 8(~9), E = (1~)3, F = 5, G = 6(~8) (E&G can be rotated, B&D can be rotated,
so 3 * 4=12 possible solutions)
5. 890A + 101B + 9C = 1100E + 1011D A = 3, B = 5, C = 4, D = 1, E = 2

5. 22 Jul '05 07:131 edit
Originally posted by Florrat
these are the solutions (2 and 4 have multiple answers...):

1. 10A + 100C + 45D = 44B A = 3, B = 5, C = 1, D = 2
2. 1000A + B = 111C + D A = 1, B = 2~7 = D-1, C = 9, D = 3~8 = B+1 (6 possible solutions)
3. 1009A + 91B = 2201C + ...[text shortened]... B + 9C = 1100E + 1011D A = 3, B = 5, C = 4, D = 1, E = 2

Well done
6. 22 Jul '05 08:552 edits
Some more for you to toss around.

-----,VW
-*---GT
_________
-----IW
---VW
_________
---TVW
7. 22 Jul '05 13:06
Originally posted by phgao
Some more for you to toss around.

-----,VW
-*---GT
_________
-----IW
---VW
_________
---TVW
you have this in your puzzle twice:
_________

what do you need to do + - * (dunno the english names ðŸ˜‰)
8. 23 Jul '05 02:19
Originally posted by Florrat
you have this in your puzzle twice:
_________

what do you need to do + - * (dunno the english names ðŸ˜‰)
Yeah, its *. Multiply. Sorry...
9. 23 Jul '05 09:26
Originally posted by phgao
Some more for you to toss around.

-----,VW
-*---GT
_________
-----IW
---VW
_________
---TVW
Sorry, I hated this primary school stuff, how you wrote all these stupid things down:
what you have to do?
-----,VW * (- * ---GT) = -----IW + ---VW = ---TVW
or do you lose information now?
Is this even possible? (if you multiply the lowest numbers with both at least 5 digits, you should get at least 9 digits)
10. 23 Jul '05 09:381 edit
Originally posted by Florrat
Sorry, I hated this primary school stuff, how you wrote all these stupid things down:
what you have to do?
-----,VW * (- * ---GT) = -----IW + ---VW = ---TVW
or do you lose information now?
Is this even possible? (if you multiply the low ...[text shortened]... ers with both at least 5 digits, you should get at least 9 digits)
Ok... since my typing isnt up to scratch, ill try to explain...

the "........" and ",,,,,,"s dont mean anything. This is a multiplication, only look at the letters. I use "........"s so they line up. That is how the sum multiplies out when completed. _______ is just a line separating the top middle and bottom of the multiplication.
11. 23 Jul '05 14:102 edits
Originally posted by phgao
Some more for you to toss around.

-----,VW
-*---GT
_________
-----IW
---VW
_________
---TVW
musn't that 'IW' have 3 digits, because I solved it so far:

VW
GT
*________
IW
VW0
+________
TVW

T = 6 because W*T=W or W+10, W+20, W+30, W+40 so T = 1 or 6. T can’t be 1 because T*V= I
V = 5 because IW+VW0=6VW and V can’t be 6 because T=6
G must be 1, because 10*G*5W=5W0 so G*5W=5W so G=1
I+W=(65-50=)15. T=6 so they must be 7 or 8

W = 7 or 8
T = 6
G = 1
V = 5
I = 7 or 8

5W
16
*________
IW
5W0
+________
65W

6*5W=IW (isn't it?)
6*5W=>300 (is larger than or equal to)
so IW => 300 but has just 2 digits... (maybe I solved it wrong...)
12. 24 Jul '05 08:082 edits
Originally posted by Florrat
musn't that 'IW' have 3 digits, because I solved it so far:

VW
GT
*________
IW
VW0
+________
TVW

T = 6 because W*T=W or W+10, W+20, W+30, W+40 so T = 1 or 6. T can’t be 1 because T*V= I
V = 5 because IW+VW0=6VW and V can’ ...[text shortened]... so IW => 300 but has just 2 digits... (maybe I solved it wrong...)
Ans : 25 * 13 = 325.