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| Temperature Reflection 2 (Posted on 2022-01-19) |
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A and B are base-α digits from 1 to α-1. Determine all triplets (A,B,α) with 2 ≤ α ≤ 36 that satisfy this relationship:
(AB)base α degrees Celsius
= (BA)base α degrees Fahrenheit
Notes:
(1) F = (9/5)*C + 32base 10, where F denotes degree(s) Fahrenheit and C denotes degrees Celsius.
(2) Each of AB and BA denotes concatenation of digits.
(3) α is a positive integer.
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Submitted by K Sengupta
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Rating: 5.0000 (1 votes)
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Solution:
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(Hide)
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The required triplets are:
(A,B,α) = (6,E,16), (2,6,17), (8,H,21), (A,K,29), and (8,G,33)
For an explanation, refer to the solution submitted by Charlie in this location.
The said solution also deals with the situation where rounding is permissible.
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