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| ABSENT TONE (Posted on 2005-09-02) |
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Each of the letters A,E,F,H,O,R,T,W,and X represents a different digit from 0 to 9 in the addition below. Can you find out which letters represent which numbers?
WORTH
THE
+EXTRA
------
EFFORT
Solution
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Comment 20 of 20 | 
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I ran this for every base from 10 to 36, but only allowing values 0 to 9 and with no leading zeros: there was only one solution in one base.
In base 11: only solution 9 3 5 4 6 + 4 6 1 + 1 7 4 5 8 -------------- 1 0 0 3 5 4
A O R T E F W H X 8 3 5 4 1 0 9 6 7
--------------- for base in range(10,37): print(base) for A in range(0,10): for O in range(0,10): if O==A: continue for R in range(0,10): if R in [A,O]: continue for T in range(1,10): if T in [A,O,R]: continue for E in range(1,10): if E in [A,O,R,T]: continue for F in range(0,10): if F in [A,O,R,T,E]: continue for W in range(1,10): if W in [A,O,R,T,E,F]: continue for H in range(0,10): if H in [A,O,R,T,E,F,W]: continue for X in range(0,10): if X in [A,O,R,T,E,F,W,H]: continue worth = W*base**4 +O*base**3 +R*base**2 +T*base+H the = T*base**2 +H*base +E extra = E*base**4 +X*base**3 +T*base**2 +R*base+A effort = E*base**5 +F*base**4 +F*base**3 +O*base**2 +R*base+T if worth+the+extra == effort: print('base', base) print(W,O,R,T,H) print(T,H,E) print(E,X,T,R,A) print(E,F,F,O,R,T) # print(worth,the,extra,effort) print(A,O,R,T,E,F,W,H,X)
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Posted by Larry
on 2024-02-25 23:11:11 |
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