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| A DEEP ROOT Problem (Posted on 2006-09-17) |
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A four digit positive decimal number DEEP ( in which each of the letters D, E and P represent a different digit) is expressed in base 7, base 6 and base 5. Treating these expressions as decimal numbers, we add them together and observe that the total is 20000. What does DEEP represent?
Another four digit positive decimal number ROOT ( in which each of the letters R, O and T represent a different digit) is expressed in base 7, base 6 and base 5. Treating these expressions as decimal numbers, we add them together and observe that the total is 54321. What does ROOT represent?
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Submitted by K Sengupta
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Rating: 3.5000 (2 votes)
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Solution:
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DEEP represents 1006
DEEP10 = 1006
DEEP7= 2635; DEEP6= 4354; DEEP5 = 13011;
and, 2635+4354+13011 = 20000
BOOT represents 2337
BOOT10 = 2337
BOOT7= 6546; BOOT6= 14453; DEEP5 = 33322;
and, 6546+ 14453 + 33322 = 54321
EXPLANATION:
Please refer to Charlie's methodology provided in this location.
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Subject |
Author |
Date |
 | solution | Dej Mar | 2006-09-17 21:32:34 |
| solution | Charlie | 2006-09-17 13:55:22 |
| Solution | JLo | 2006-09-17 13:44:45 |
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