What if there are 110 coins total. Can you walk me through exactly how you end up with 2 piles of exactly the same amount of heads? And what if there are 500?
Hidden:
110 coins means 99 heads and 11 tails.
Pile A will have 99 coins, and pile B 11.
Lets assume all 99 heads are in pile A. Now that ur turning all of Pile A, there are zero heads in both piles.
Now think if there are only 98 heads in A. That means that 1 of those 99 is in pile B. But that also means that there is 1 tail in pile A. Turning all of pile A, will ensure that the single tail will revert to a head.
No matter which way it's distributed, for every one head that's not in pile A, there must be one head in pile B, cuz it has to add up to 99.
110 coins means 99 heads and 11 tails.
Pile A will have 99 coins, and pile B 11.
Lets assume all 99 heads are in pile A. Now that ur turning all of Pile A, there are zero heads in both piles.
Now think if there are only 98 heads in A. That means that 1 of those 99 is in pile B. But that also means that there is 1 tail in pile A. Turning all of pile A, will ensure that the single tail will revert to a head.
No matter which way it's distributed, for every one head that's not in pile A, there must be one head in pile B, cuz it has to add up to 99.
What if there are 110 coins total. Can you walk me through exactly how you end up with 2 piles of exactly the same amount of heads? And what if there are 500?
For 110:
Hidden:
Pile A has to have between 88 and 99 heads.
If it has 88 heads (and 11 tails), then pile B has 11 heads.
If you flip over A you get 88 tails and 11 heads.
What if there are 110 coins total. Can you walk me through exactly how you end up with 2 piles of exactly the same amount of heads? And what if there are 500?
Hidden:
If there are 500 coins, it may be that pile A won't have any of the heads. That means all 99 heads are in pile B. By flipping all of pile A, you get 99 heads as well.
If 20 heads land in Pile A, then the rest 79 are in B. Pile A will have SAME AMOUNT in tails-79. Flip all of pile A, and you get equal heads.
Pile A has to have between 88 and 99 heads.
If it has 88 heads (and 11 tails), then pile B has 11 heads.
If you flip over A you get 88 tails and 11 heads.
A major horse race is coming up, and a trainer wants to test his 25 horses, and choose his 3 fastest ones.
Every time he races his horses, the order of finish accurately reflects the relative speeds of the horses. However, he's only able to race 5 of them at a time.
What is the minimum number of races required for him to determine the three fastest horses?
A major horse race is coming up, and a trainer wants to test his 25 horses, and choose his 3 fastest ones.
Every time he races his horses, the order of finish accurately reflects the relative speeds of the horses. However, he's only able to race 5 of them at a time.
What is the minimum number of races required for him to determine the three fastest horses?
Hidden:
My first guess would be 5 assuming he also keeps track of the time it took the runners-up at every race. But this guess seems too easy
Do you want an answer without allowing the trainer to keep track of time
My first guess would be 5 assuming he also keeps track of the time it took the runners-up at every race. But this guess seems too easy
Do you want an answer without allowing the trainer to keep track of time
Without timing. Suppose he conducts each race in a different setting, some have more hills, some straight etc. Only relative speed is taken in consideration.
Without timing. Suppose he conducts each race in a different setting, some have more hills, some straight etc. Only relative speed is taken in consideration.
Oh ok so this is another hard one. Until I’ll hear the answer and say boy was this simple!
I gotta find a quicker method, I agree. Was good for Chelm.
I'll wait.
Once the answer is posted, even if hidden, it's tempting to look.
But I believe you can solve this one! Don't necessarily have to be a math giant...
I'll wait.
Once the answer is posted, even if hidden, it's tempting to look.
But I believe you can solve this one! Don't necessarily have to be a math giant...
A major horse race is coming up, and a trainer wants to test his 25 horses, and choose his 3 fastest ones.
Every time he races his horses, the order of finish accurately reflects the relative speeds of the horses. However, he's only able to race 5 of them at a time.
What is the minimum number of races required for him to determine the three fastest horses?
Edited my answer
Hidden:
8
5 races of 5 2 of each group are eliminated
Winners race each other
At this point 2 full groups plus 4 of the 3 rd place holders group are eliminated
7 still in the race
Now race 5
Top 3 race other 2
Last edited by doodlesmom on Wed, Oct 14 2020, 7:47 pm; edited 1 time in total
