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## Symbols

Math brain teasers require computations to solve.

 Puzzle ID: #4318 Fun: (2.55) Difficulty: (2.7) Category: Math Submitted By: cathalmccabe Corrected By: cnmne

Each letter ABCDEFGH represents the numbers 1 to 8 inclusive:

FA*A=CF
DG*A=BA
H*E=DH
F*A = C

Can you match the letter to the number?

### Answer

1 = G
2 = A
3 = D
4 = F
5 = H
6 = B
7 = E
8 = C

42*2=84
31*2=62
5*7=35
4*2 = 8

Solution: (From 2: means 2nd line etc:)
From 2: G=1 because A*G = A (A is not 5, because then from 1, F should also be 5)

From 4: F*A has to be a single number so it can only be 2*3 or 2*4 (or vice versa) and C can only be 6 or 8
There are four possibilities here,
4*2 = 8
2*4 = 8
3*2 = 6 or
3*2 = 6

They would give from 1:
42*2 (=84)
24*4 (=92)
32*2 (=64) or
23*3 (=69)
Can't be 2*4 or 3*2 (because 92 and 69 are not possible), so
A=2
From 2: B is twice something, so it can only be 4 6 or 8 (not 2 because it's already known)
D is half 4 6 or 8, so it can only be 2, 3, or 4

From 3: All the possible combinations of numbers multiplied that would give a two digit number: (Eliminate any with 1 or 2 in the product eg 3*7=21 or 3*8=24 etc)

4*8 =32
5*6 =30
5*7 =35
5*8 =40
6*7 =42
6*8 =48

The second term of the product must be one of the numbers multiplied by each other, so eliminate any that don't fit in here leaving:

5*7 =35
6*8 =48

So, filling in what's known so far:

F2*2=CF
D1*2=B2
H*E=DH
F*2 = C

From 1: F=4, then C = 8
From 2: B = 6
From 3: H*E = 5*7 or 5*7 = 35 D=3 H= 5, so E = 7

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## Comments

 (user deleted) Sep 18, 2002 Wow! I cant believe it, this guy got one right, whoohee at last. It was bound to happen, the law of avrages and all that!!! cluemaster Apr 01, 2009 This puzzle can be solved without the first equation. Probably can alternately be solved without the last - haven't checked. Jimbo May 05, 2009 Good puzzle. Well explained. Neat! chunnie May 12, 2013 [quote]Solution: (From 2: means 2nd line etc From 2: G=1 because A*G = A [/quote] Why is A*G=A?

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