### Brain Teasers

# Symbols

Math
Math brain teasers require computations to solve.

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?

FA*A=CF

DG*A=BA

H*E=DH

F*A = C

Can you match the letter to the number?

### Hint

G = 1### Answer

1 = G2 = 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

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!!!

This puzzle can be solved without the first equation. Probably can alternately be solved without the last - haven't checked.

Good puzzle. Well explained. Neat!

[quote]Solution: (From 2: means 2nd line etc

From 2: G=1 because A*G = A [/quote]

Why is A*G=A?

From 2: G=1 because A*G = A [/quote]

Why is A*G=A?

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