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| Numbers À Propos (Posted on 2005-09-20) |
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If letters are assigned the values A=1, B=2, ..., Z=26, then any word will have a total value equal to the total of the values of its letters.
Doing this will give square a value of 81, which is a perfect square. The word prime will have a value of 61, which is prime. Also, odd will evaluate as 23, which is odd, and even as 46, which is even.
If we were to change the values of three of the letters of the alphabet, so that the other 23 letters had the same values as above, but the chosen three had their values scrambled, words would have different values. An example of scrambling the values of three letters would be if I chose B, E and H, to give B=8 (ordinarily the value for H), E=2 (ordinarily the value for B) and H=5 (ordinarily the value for E).
With a particular scrambling of the values of some three letters, square has a different value, but is still a perfect square; prime has a lower value but is still a prime; and odd is still odd and even still even, though at least one of odd or even has a different value from before.
What are the three letters that had their values changed, and what are those values?
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Submitted by Charlie
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Rating: 4.2000 (5 votes)
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Solution:
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(Hide)
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The solution is that d has the value 21; u has the value 18 and r has the value 4, giving square the value 64, prime the value 47 and odd the value 57 while even retains the value 46.
This was New Scientist magazine's Enigma # 1347, composed by Susan Denham, published in the July 2-8, 2005 issue.
Found by the program
DECLARE FUNCTION eval! (s$)
DATA 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,79, 83, 89, 97, 101, 103, 107, 109, 113, 127
DIM pr(31)
FOR i = 1 TO 31: READ pr(i): NEXT
DIM SHARED l1, l2, l3, alpha$
CLS
alpha$ = "abcdefghijklmnopqrstuvwxyz"
q0 = eval("square")
p0 = eval("prime")
o0 = eval("odd")
e0 = eval("even")
PRINT q0; p0; o0; e0
PRINT
FOR l1 = 1 TO 26
s1$ = MID$(alpha$, l1, 1)
q1 = INSTR("square", s1$) > 0
p1 = INSTR("prime", s1$) > 0
o1 = INSTR("odevn", s1$) > 0
FOR l2 = 1 TO 26
IF l2 > l1 THEN
s2$ = MID$(alpha$, l2, 1)
q2 = INSTR("square", s2$) > 0
p2 = INSTR("prime", s2$) > 0
o2 = INSTR("odevn", s2$) > 0
FOR l3 = 1 TO 26
IF l3 > l1 AND l3 <> l2 THEN
s3$ = MID$(alpha$, l3, 1)
q3 = INSTR("square", s3$) > 0
p3 = INSTR("prime", s3$) > 0
o3 = INSTR("odevn", s3$) > 0
IF (q1 OR q2 OR q3) AND (p1 OR p2 OR p3) AND (o1 OR o2 OR o3) THEN
q = eval("square")
p = eval("prime")
o = eval("odd")
e = eval("even")
qr = INT(SQR(q) + .5)
IF qr * qr = q THEN
good = 0
FOR i = 1 TO 31
IF pr(i) = p THEN
good = 1: EXIT FOR
END IF
NEXT i
IF good THEN
IF q <> q0 AND p < p0 AND (o <> o0 OR e <> e0) THEN
IF o MOD 2 = 1 AND e MOD 2 = 0 THEN
PRINT l1; l2; l3, s1$; s2$; s3$
PRINT q; p; o; e
PRINT
END IF
END IF
END IF
END IF
END IF
END IF
NEXT
END IF
NEXT
NEXT
FUNCTION eval (s$)
t = 0
FOR i = 1 TO LEN(s$)
v = INSTR(alpha$, MID$(s$, i, 1))
IF v <> l1 AND v <> l2 AND v <> l3 THEN
t = t + v
ELSE
SELECT CASE v
CASE l1
t = t + l2
CASE l2
t = t + l3
CASE l3
t = t + l1
END SELECT
END IF
NEXT
eval = t
END FUNCTION
and printed out as
81 61 23 46
4 21 18 dur
64 47 57 46
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