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Radar decoded (Posted on 2023-07-01) Difficulty: 2 of 5
SOLVE:

RADAR=(R+A+D)^4

Each letter stands for a certain digit.

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution Comment 9 of 9 |
RADAR is the fourth power of R+A+D.  Also 10^4 < RADAR < 10^5.
Then take the fourth roots to get 10 < (R+A+D) < 17.8.
Then R+A+D is limited to 11,12,13,14,15,16,17.

At this point its pretty easy to compute the fourth powers of the seven integers:
11^4 = 14641
12^4 = 20736
13^4 = 28561
14^4 = 38416
15^4 = 50625
16^4 = 65536
17^4 = 83521

The only one that matches the pattern RADAR is 14641, and in this case R+A+D does evaluate to 11.  So then the answer is 14641 = (1+4+6)^4.

  Posted by Brian Smith on 2023-07-02 16:21:47
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