Question 429.
Suppose 3 four digits numbers with base seven were added and the 3rd four digit number was hidden, that I could not see it but the resulting number with base seven that was obtained when the 3 four digit numbers were added, was given. Find the 3rd four digit number (with base seven) using the information given.
4321+1234+****=12341.
Answer 429.
4321 base 7
= 1*7^0 + 2*7^1 + 3*7^2 + 4*7^3
= 1 + 14 + 147 + 1372
= 1534
1234 base 7
= 4*7^0 + 3*7^1 + 2*7^2 + 1*7^3
= 4 + 21 + 98 + 343
= 466
12341 base 7
= 1*7^0 + 4*7^1 + 3*7^2 + 2*7^3 + 1*7^4
= 1 + 28 + 147 + 686 + 2401
= 3263
=> missing number in base 10 is
3263 - 1534 - 466
= 1263
Noting that 7^0 = 1, 7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401
1263
= 3*7^3 + 4*7^2 + 5*7^1 + 3*7^0
= 3453 (base 7) <=== Answer.
Link to YA!
Suppose 3 four digits numbers with base seven were added and the 3rd four digit number was hidden, that I could not see it but the resulting number with base seven that was obtained when the 3 four digit numbers were added, was given. Find the 3rd four digit number (with base seven) using the information given.
4321+1234+****=12341.
Answer 429.
4321 base 7
= 1*7^0 + 2*7^1 + 3*7^2 + 4*7^3
= 1 + 14 + 147 + 1372
= 1534
1234 base 7
= 4*7^0 + 3*7^1 + 2*7^2 + 1*7^3
= 4 + 21 + 98 + 343
= 466
12341 base 7
= 1*7^0 + 4*7^1 + 3*7^2 + 2*7^3 + 1*7^4
= 1 + 28 + 147 + 686 + 2401
= 3263
=> missing number in base 10 is
3263 - 1534 - 466
= 1263
Noting that 7^0 = 1, 7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401
1263
= 3*7^3 + 4*7^2 + 5*7^1 + 3*7^0
= 3453 (base 7) <=== Answer.
Link to YA!
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