Question

Discrete Structures problem

Suppose we have an unlimited supply of five-ounce weights and an unlimited supply of eight-ounce weights. Show by strong induction that we can combine weights of these types to make any whole number of ounces greater than or equal to _________. (You should fill in the blank with the smallest whole number that works before starting your proof. ) As an example, we can make a total of 10 ounces using two five-ounce weights or we could make a total of 8 ounces using one eight-ounce weight, but we can't make 9 ounces or 11 ounces.

Answer 1

We have un limited supply five-ou ounce weights 11 eight 1/ Now Problem is to find the miniman nomber of weights required to measure any weights А B weighting machine & 1 then it by combination of 5 leg weight & & kg weights we could measure 1kg could measure by repeation of weighting process. wooof weight 5 kg no.ofweight bry Possible weight coul we - 8kg,5kg, 3 k 2 18kg, akg , long , 2 ou 2 S ,16 ,21,1 10 , 16, 26, 2 2 2 whole no. 3 13,16,81 Ok9 minimum non of weights regiused to ang is 5 weight (3-5 mevcichts How to measure 2- B kg weigts Put * 2 Brq weights at A 3 Sky wergth at B diff = (2x8)-(3x) = 1 kg pelo to balance weighting machine ( a 1 Put I more kg at B sille

at B You It it got balance ince the substance you are puting weighs 1 kg: Can weigh any whole no. weight by repeating the weight measurement by 1 kg difference make any other combination Eg weight atg take this 5 kg ina ad one 8 kg in B take I 8 kg in A and one skg in B u Nog take 3 bkg in A ad ae 5 kg in B 08 con 3 kg 9 kg 3 - 5 kg in A 3-8kg MB 1 - 5 kg in B : 1 kg 2-8kg in A Ans 1 NOTE: You may inspite of kg use welight unit as ounce