+0  
 
-2
107
8
avatar

1.  For a certain base b, the product (12 subscript b)(15 subscript b)(16 subscript b) is equal to 3146 subscript b. Let S = 12 subscript b + 15 subscript b + 16 subscript b. What is S in base b?

 

 

 

2. Let b be an integer greater than 2, and let N subscript b = 1 subscript b + 2 subscript b + .... + 100 subscript b (the sum contains all valid base b numbers up to 100 subscript b). Compute the number of values of b for which the sum of the squares of the base b digits of N subscript b is at most 512.

 

 

 

3.  Let a subscript 2, a subscript 1, and a subscript 0 be three digits. When the 3-digit number a-sub2,a-sub1,a-sub0 is read in base b and converted to decimal, the result is 254. When the 3-digit number a-sub2,a-sub1,a-sub0 is read in base b+1 and converted to decimal, the result is 330. Finally, when the 3-digit number a-sub2,a-sub1,a-sub0 is read in base b+2 and converted to decimal, the result is 416. Find the 3-digit number a-sub2,a-sub1,a-sub0. (Express your answer in decimal.)

 

 

4.  Consider the set S = {0, 1, 2, ... , 3^k-1}. Prove that one can choose T to be a 2^k-element subset of S such that none of the elements of T can be represented as the arithmetic mean of two distinct elements of T.

 Mar 26, 2020
edited by Guest  Mar 26, 2020
 #1
avatar+21017 
0

I really can't read this.

 Mar 26, 2020
 #2
avatar
0

convert it into latex

Guest Mar 26, 2020
 #3
avatar+24 
0

The latex for me doesn't work. I can't copy and paste the questions into the latex bar. It just makes more junk.

inomath  Mar 26, 2020
 #4
avatar
0

the problem has been edited so it is readable now

Guest Mar 26, 2020
 #5
avatar+21017 
0

For problem #1, b = 9. Can you finish the problem?

 Mar 26, 2020
 #6
avatar
0

i know that b is 9 but I plugged in the values and got 40 for s

Guest Mar 26, 2020
 #8
avatar+21017 
0

129 + 159 + 169  =  11 + 14 + 15  =  40

geno3141  Mar 26, 2020
 #7
avatar+21017 
0

3)  base b is 7; base b + 1 is 8; base b + 2 is 9

 Mar 26, 2020

6 Online Users