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Square alphametics (Posted on 2019-01-06) Difficulty: 3 of 5
FOUR and NINE are square numbers, both have the same sum of digits i.e. IN

ONE is not a square, but its s.o.d. is. It equals IE.

Each of the bold letters represents a digit in a one-to-one correspondance.
What is the value of FINE?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution Too Much Info (Analytical Solution) Comment 1 of 1
a) O+N+E = 10*I + E, so O+N = 10*I, so I = must equal 1

b) IE is square, so E must = 6

c) N+I+N+E = 10*I + N, so 2*N +7 = 10 + N, so N = 3
    Checking, NINE =  3136 = 56^2.
    We did not need to know that this was square to solve the alphametic.

d) O + N = 10, so O = 7

e) F+O+U+R = 13, so F+U+R = 6
    Since 1 and 3 are accounted for, this can only be 0, 2 and 4 in some order.
    FOUR must equal 2704 or 2740 or 4702 or 4720.  
    Only 2704 is square, being 52^2.

f) So FINE = 2136.  It is not square, and neither is its s.o.d.

  Posted by Steve Herman on 2019-01-06 08:32:45
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