Thread - 26-Letter Puzzle Contest - LMI Monthly Test July 2026

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randomperson1729 - 2026-07-10 11:06 AM

For Balance (#11 on the IB): how exactly is the torque of the main rod calculated with regard to weights on attached rods (i.e. the two bottom rods on the main example)? When I first read the instructions, I thought each subordinate rod's torque on the main rod was calculated by adding the torque of both sides of the smaller rod and multiplying it by the distance of that rod's fulcrum to the main rod's fulcrum, but the math only balances out if you instead use each weight's horizontal distance to the main fulcrum without regard to vertical distance: with the former you get 2*5 _PLUS_ 1(2*2_PLUS_1*4) =! 4(3*1_PLUS_1*3), while with the latter you get 2*5_PLUS_3*2_PLUS_0*4=1*1_PLUS_5*3.

For all the lower rods, you use the lower rod's attachment point on the upper rod. So it reads (distance 2 * weight 5) _PLUS_ (distance 1 * (weight 2_PLUS_4)) = (distance 4 * (weight 1_PLUS_3)).


Restricted Thread This is a restricted thread corresponding to an ongoing contest at LMI. This mainly means : Comments posted in the thread after the contest started can only be viewed by players who have finished the contest. If you are not logged in to forum or if you have not finished the contest, you will see first few characters of the post. The purpose is to encourage players to freely post comments while the contest is running. Admins can make the post public before the contest is over, if it does not reveal anything about the puzzles. All the posts will be made public after the contest is over.
	@ 2026-07-10 11:06 AM (#41016 - in reply to #41015) (#41016) Top
chaotic_iak Posts: 243 Country : Indonesia	chaotic_iak posted @ 2026-07-10 11:06 AM randomperson1729 - 2026-07-10 11:06 AM For Balance (#11 on the IB): how exactly is the torque of the main rod calculated with regard to weights on attached rods (i.e. the two bottom rods on the main example)? When I first read the instructions, I thought each subordinate rod's torque on the main rod was calculated by adding the torque of both sides of the smaller rod and multiplying it by the distance of that rod's fulcrum to the main rod's fulcrum, but the math only balances out if you instead use each weight's horizontal distance to the main fulcrum without regard to vertical distance: with the former you get 25 _PLUS_ 1(22_PLUS_14) =! 4(31_PLUS_13), while with the latter you get 25_PLUS_32_PLUS_04=11_PLUS_53. For all the lower rods, you use the lower rod's attachment point on the upper rod. So it reads (distance 2 * weight 5) _PLUS_ (distance 1 * (weight 2_PLUS_4)) = (distance 4 * (weight 1_PLUS_3)).