30 flasks--10 full, 10 half-empty, and 10 entirely empty--are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?
pour half of each of the 10 full flasks into the 10 empty cans
you now have 30 half-full flasks, so each gets 10
half-full flasks
To divide the flasks and their contents equally among the three sons, each son should receive the same number of flasks and an equal distribution of the varying levels of contents.
Step 1: First, let's divide the full flasks equally among the three sons. Each son will receive 10 full flasks/3 = 3 full flasks.
Step 2: After dividing the full flasks, we are left with 20 flasks—10 half-empty and 10 completely empty flasks. We'll distribute these among the three sons as follows:
- Son 1: Since there are 10 half-empty flasks remaining, Son 1 will receive 10 half-empty flasks/3 = 3 flasks. Additionally, Son 1 will also receive 1 more flask from the 10 completely empty flasks, making a total of 3 flasks + 1 flask = 4 flasks for Son 1.
- Son 2: There are also 10 half-empty flasks remaining, so Son 2 will receive 10 half-empty flasks/3 = 3 flasks. Since Son 1 already received 1 empty flask, Son 2 will receive 1 empty flask as well from the remaining 9 empty flasks, making a total of 3 flasks + 1 flask = 4 flasks for Son 2.
- Son 3: Similarly, Son 3 will receive 10 half-empty flasks/3 = 3 flasks. Since both Son 1 and Son 2 received 1 empty flask each, Son 3 will receive 1 empty flask from the remaining 8 empty flasks, making a total of 3 flasks + 1 flask = 4 flasks for Son 3.
Step 3: After following the above distribution, each son will have an equal number of flasks and an equal distribution of the varying levels of contents:
- Son 1: 3 full flasks + 1 half-empty flask + 1 empty flask = 5 flasks
- Son 2: 3 full flasks + 1 half-empty flask + 1 empty flask = 5 flasks
- Son 3: 3 full flasks + 1 half-empty flask + 1 empty flask = 5 flasks
Therefore, each son will have 5 flasks, with an equal share of the full, half-empty, and empty flasks.
To divide the flasks and their contents equally among the 3 sons, we need to follow a step-by-step approach:
Step 1: Start with the 10 entirely empty flasks. Give each son 3 flasks. This way, each son will have 3 empty flasks.
Step 2: Now, let's consider the 10 half-empty flasks. Each half-empty flask can be combined with another half-empty flask to make one full flask. We have a total of 10 half-empty flasks, which means that we can make 5 full flasks. Distribute these 5 full flasks equally among the 3 sons. Initially, each son had 3 empty flasks, so now they will each have an additional 1 full flask.
Step 3: Finally, we are left with 10 full flasks. Distribute these equally among the 3 sons. Each son will receive 3 full flasks.
To summarize:
- Each son will receive 3 empty flasks initially.
- After combining the half-empty flasks and distributing them equally, each son will have 1 full flask in addition to their 3 empty flasks.
- Finally, distribute the remaining 10 full flasks equally among the 3 sons, giving each son a total of 3 full flasks.
Following this plan, each son will have an equal number of flasks and an equal share of their contents.