Question

How many numbers can be maximally chosen from the numbers 5, 10, 15, .., 95, 100 such that no two chosen numbers sum to 105?

Answer 1

Answer:

i think its 10

Step-by-step explanation:

5+100=105,10+95=105 ect ect but there are 20 numbers right? so i think you can choose a maximum of 10! hope it helps if it doesn't sorry

Answer 2

To find

Maximum numbers that can be chosen from the series 5, 10, 15, ....., 95, 100 where no two numbers sum up to 105.

Solution

We see that the sum of:

5 and 100 = 105, that is 5 + 100 = 105, so we take only one from it.

Similarly, we see pairs of (10, 95), (15, 90), (20, 85), (25, 80), (30, 75), (35, 70), (40, 65), (45, 60), and (50, 55), and take only one number from these pairs so that we don't end up with a sum of 105 of any two numbers.

As we get 10 such pairs and no numbers are left, we can conclude that:

A maximum of 10 numbers can be selected from the given series so that no two chosen numbers sum to 105.

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