Write the odd integers in order up to 35.

Question

Write the odd integers in order up to 35. The first number after 1 is 3, so strike out every 3rd integer in the list. The next smallest number is now 7; strike out every 7th number from the list that remains. The numbers that remain are called lucky numbers. Find four ways to write 34 as the sum of two lucky numbers.

Answer 1

1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35

strike every 3rd number leaving

1,3, 7,9, 13, 15, 19,21, 25,27, 31,33

strike every 7th number remaining, that just removes 19

1,3,7,9,13,15, 21, 25, 27, 31, 33 (but the next smallest number is 3 not 7)

34=33+1 or = 31+3 or = 27+7 or = 25+9 or 21+13

34 = sum of last and first in the remaining numbers

= sum of 1st and 11th numbers

or sum of 2nd to last and 2nd= sum of 2nd and 10th

or sum of 3rd to last and 3rd= sum of 3rd and 9th

or sum of 4th to last and 4th - sum of 4th and 8th

or sum of 5th to last and 5th= sum of 5th and 7th