Alphametics - Involving Multiplication
Alphametics - Involving Multiplication
Search for "1" in multiplications
Introduction : - In this multiplication :
The first partial product is E MAD = MAD. Hence, "E" must equal "1". This is called the "identity" property of "1" in multiplication; you multiply anything by "1" and it doesn't change, therefore it remains the same.
Search for "1" and "6" in multiplications
Any number multiplied by "1" is the number itself. Also, any even number multiplied by "6" is the number itself.
Looking at right hand digits of multiplications can help you spot digits "1" and "6". The logic is : if
Then, A = 1 or A = 6.
Search for "0" and "5" in multiplications
Any number multiplied by zero is zero. Also, any odd number multiplied by "5" is "5" :
Looking at right hand digits of multiplications can help you spot digits "0" and "5". The logic is : if
Then A = 0 or A = 5
Illustration: In the following question on multiplication, each letter always stands for the same digit.
For which digit does "D" stand ?
A. 3 B. 8 C. 9 D. 7
Answer : A
Solution : - P = 0, because S + 0 = S
M + M = P, which implies M = 5, because P = 0
A A = M = 5, so, A = 2, because 1 is carry.
D D = S, which is 1 digit number, D cannot be 1 or 2. Hence, D = 3
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