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How many unique sums can be formed by adding any three different numbers from the set {4,6,8,10,12,...,154}?

 Feb 8, 2024

Best Answer 

 #1
avatar+1632 
+2

The smallest number that can be formed is 4 + 6 + 8 = 18, and the largest: 150 + 152 + 154 = 456.

Note how every even number up to 456 can be formed: for example, 20 = 18 + 2 = 4 + 6 + 8 + 2 = 4 + 6 + 10... 164 = 4 + 6 + 154

166 = 4 + 8 + 154... 168 = 6 + 8 + 154... 170 = 6 + 10 + 154... so on- until you reach the largest number that can be formed.

Okay, so now we know that all the even numbers 18 to 456 inclusive can be formed: how many numbers are in this list?

# of numbers {18,..., 456} = # of numbers {18 - 18,...,456 - 18 = 438} = {0/2,...,438/2} = {0,...,219} = {0 + 1,...,219 + 1} = 1 through 220 inclusive.

 

So, the answer is 220.

 Feb 8, 2024
 #1
avatar+1632 
+2
Best Answer

The smallest number that can be formed is 4 + 6 + 8 = 18, and the largest: 150 + 152 + 154 = 456.

Note how every even number up to 456 can be formed: for example, 20 = 18 + 2 = 4 + 6 + 8 + 2 = 4 + 6 + 10... 164 = 4 + 6 + 154

166 = 4 + 8 + 154... 168 = 6 + 8 + 154... 170 = 6 + 10 + 154... so on- until you reach the largest number that can be formed.

Okay, so now we know that all the even numbers 18 to 456 inclusive can be formed: how many numbers are in this list?

# of numbers {18,..., 456} = # of numbers {18 - 18,...,456 - 18 = 438} = {0/2,...,438/2} = {0,...,219} = {0 + 1,...,219 + 1} = 1 through 220 inclusive.

 

So, the answer is 220.

proyaop Feb 8, 2024

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