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# Sum and Difference

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Numbers are drawn from 1,500 integers between 135 and 1,634. What is the least number of integers that must be randomly drawn to ensure that there are two numbers whose difference is 149 and whose sum is also 149? Thank you for help.

Jun 9, 2022

#1
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two numbers in this range can't sum to 149

there is an error in the question

Jun 9, 2022
#2
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You are absolutely right! That is because of a typo in "sum of 149"! It should read: 949. Thanks.

Guest Jun 9, 2022
#3
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1 - Minimum number if integers needed so that at least 2 sum up to 949 is calculated as follows:
1,500 - ceil(949/2) + 2 ==1,027 integers.

2 - Minimum number of integers needed so that at least 2 of them will have a difference of 149 is calculated as follows:
a - If the integer of (1,500/149) mod 2==0[i.e. EVEN], then:
[Ceil(1,500/149) / 2 * 149] + [1,500 mod 149] + 1==756 integers [which is the answer to this particular question]

b - If the integer of (1,500 / 149) mod 2 ==1[i.e., ODD such as (1,500/165), then:
Int[(1,500 / 165) + 1] / 2 * 165 + 1==826 integers [for this hypothetical example]

Jun 10, 2022