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A363802
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Numbers whose digits can be interposed with one or more of the arithmetic operators +, -, *, /, with no parentheses or concatenation, to yield 10 as the result.
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0
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19, 25, 28, 37, 46, 52, 55, 64, 73, 82, 91, 109, 118, 119, 125, 127, 128, 133, 136, 137, 145, 146, 152, 154, 155, 163, 164, 172, 173, 181, 182, 190, 191, 208, 215, 217, 218, 219, 224, 226, 229, 234, 235, 242, 244, 250, 251, 253, 262, 271, 274, 280, 281, 286, 291, 298, 307
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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This sequence is a variant of a "game" you can play using the numbers on train carriages (usually 4 digits in Australia's case), ignoring prefixed zeros, preventing re-ordering of the digits and allowing only addition, subtraction, multiplication and division.
No parentheses or concatenation are allowed and expressions follow operator precedence (*/) then (+-), and left to right within the same level of precedence: "2 + 3 * 2 / 6" is 2 + ((3*2)/6) = 2 + 1 = 3.
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LINKS
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EXAMPLE
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1 + 9 = 2 + 8 = 1 * 9 + 1 = 2 * 9 - 8 = 10 so 19, 28, 191 and 298 are terms.
110 is not a term even though 1 * 10 = 10 since concatenation is disallowed.
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PROG
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(Python)
from itertools import product
from fractions import Fraction
s = [f"Fraction({d}, 1)" for d in str(n)]
for ops in product("+-*/", repeat=len(s)-1):
try: v = eval("".join(sum(zip(ops, s[1:]), (s[0], ))))
except: v = None
if v == 10: return True
return False
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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