1. Count 16 Hrs
John has a small and a large hourglasses. The small one can measure 5 minutes and the large one can measure 7 minutes. How can he measure 16 minutes with 2 hourglasses running together?
The rule is when any one of the hourglasses finishes leaking, that hourglass must be flipped over immediately to keep it running
Ans. Steps Below
7m 5m
2/5 0/5 => Tot =5
0/7 3/2 => Tot = 7
5/2 0/5 => Tot = 9. Here flip the 7m glass
0/7 0/5 => Tot =11. Flip 5 min glass
0/7 0/5 => Tot =16
2. Which egg is lighter
Eight eggs look identical except one is lighter. How can you weigh only 2 times on a balance scale to find out which one is lighter?
Ans. Split into 3 groups 3-3-2.
Measure 3 against 3.
If they are of same weight:
lighter ball is among 2 ball, weigh them to find the lighter ball. (So total weighed 2 time)
Else 3-3 are of different weight, take the lighter pile
weight 1-1, if they are same, left out ball is lightest. Otherwise you know it (total in this case too 2 time)
3. Which coin is lighter
There are 80 pieces of gold. One of them is lighter. You can weigh only 4 times to find out which one is lighter
Ans. Based on same concept as question number 2 above.
One of many solution is below.
Slit 30-30-20.
Weight 1: 30-30
Case 1: they are equal, then coin is in 20's pile
Split 8-8-4
As you know this problem is same as question number 2 which takes 2 weighs to find out the lightest. So total weight would be 1+2 = 3. Means we are game.
Case2: one of the 30's pile is light.
split 12-12-6
Weight 2: 12-12
if one of the 12's pile is ligher
split 8-4. Which again is problem number 2 and max weights would be 2+2 =4.
Finding lightest among 6 coins is again 2 weighs.
Problem is solved.
4. Cross the Bridge
There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each woman walks at a different speed. A pair must walk together at the rate of the slower woman's pace.
Woman 1: 1 minute to cross
Woman 2: 2 minutes to cross
Woman 3: 5 minutes to cross
Woman 4: 10 minutes to cross
For example if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Woman 4 then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. What is the order required to get all women across in 17 minutes? Now, what's the other way?
Ans.
1,2,5,10----------------------
5,10--------------------------1,2 Tot =2 mins
1,5,10-------------------------2, tot = 3 mins
1-------------------------------2,5,10, tot = 13 min
1,2-----------------------------5,10, tot =15min
---------------------------------1,2,5,10 tot =17 min
5. Ratio of color in bucket
If you have two buckets, one with red paint and the other with blue paint, and you take one cup from the blue bucket and poor it into the red bucket. Then you take one cup from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio between red and blue? Prove it mathematically.
Ans. Same
let the volume of buckets be 2 L each represented by 2x and 2y ( x for bucket 1 and y for bucket 2).
so initially A=2x , B=2y
let the volume of cup be x.
so after [ step 1 ] : one cup red paint from bucket 1 to 2
A=x L and B = xL + 2yL.
so ratio of paints Red:Blue in red bucket = 1:2
[step 2] : one cup paint from bucket 2 to 1
so B = x + 2y - [ (1/3)x + (2/3)y ] = 2x/3 + 4y/3
and A= x + [ (1/3)x + (2/3)y ] = 4x/3 + 2y/3
so coeff of x in a = coeef of y in B.
More puzzles follow here
John has a small and a large hourglasses. The small one can measure 5 minutes and the large one can measure 7 minutes. How can he measure 16 minutes with 2 hourglasses running together?
The rule is when any one of the hourglasses finishes leaking, that hourglass must be flipped over immediately to keep it running
Ans. Steps Below
7m 5m
2/5 0/5 => Tot =5
0/7 3/2 => Tot = 7
5/2 0/5 => Tot = 9. Here flip the 7m glass
0/7 0/5 => Tot =11. Flip 5 min glass
0/7 0/5 => Tot =16
2. Which egg is lighter
Eight eggs look identical except one is lighter. How can you weigh only 2 times on a balance scale to find out which one is lighter?
Ans. Split into 3 groups 3-3-2.
Measure 3 against 3.
If they are of same weight:
lighter ball is among 2 ball, weigh them to find the lighter ball. (So total weighed 2 time)
Else 3-3 are of different weight, take the lighter pile
weight 1-1, if they are same, left out ball is lightest. Otherwise you know it (total in this case too 2 time)
3. Which coin is lighter
There are 80 pieces of gold. One of them is lighter. You can weigh only 4 times to find out which one is lighter
Ans. Based on same concept as question number 2 above.
One of many solution is below.
Slit 30-30-20.
Weight 1: 30-30
Case 1: they are equal, then coin is in 20's pile
Split 8-8-4
As you know this problem is same as question number 2 which takes 2 weighs to find out the lightest. So total weight would be 1+2 = 3. Means we are game.
Case2: one of the 30's pile is light.
split 12-12-6
Weight 2: 12-12
if one of the 12's pile is ligher
split 8-4. Which again is problem number 2 and max weights would be 2+2 =4.
Finding lightest among 6 coins is again 2 weighs.
Problem is solved.
4. Cross the Bridge
There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each woman walks at a different speed. A pair must walk together at the rate of the slower woman's pace.
Woman 1: 1 minute to cross
Woman 2: 2 minutes to cross
Woman 3: 5 minutes to cross
Woman 4: 10 minutes to cross
For example if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Woman 4 then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. What is the order required to get all women across in 17 minutes? Now, what's the other way?
Ans.
1,2,5,10----------------------
5,10--------------------------1,2 Tot =2 mins
1,5,10-------------------------2, tot = 3 mins
1-------------------------------2,5,10, tot = 13 min
1,2-----------------------------5,10, tot =15min
---------------------------------1,2,5,10 tot =17 min
5. Ratio of color in bucket
If you have two buckets, one with red paint and the other with blue paint, and you take one cup from the blue bucket and poor it into the red bucket. Then you take one cup from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio between red and blue? Prove it mathematically.
Ans. Same
let the volume of buckets be 2 L each represented by 2x and 2y ( x for bucket 1 and y for bucket 2).
so initially A=2x , B=2y
let the volume of cup be x.
so after [ step 1 ] : one cup red paint from bucket 1 to 2
A=x L and B = xL + 2yL.
so ratio of paints Red:Blue in red bucket = 1:2
[step 2] : one cup paint from bucket 2 to 1
so B = x + 2y - [ (1/3)x + (2/3)y ] = 2x/3 + 4y/3
and A= x + [ (1/3)x + (2/3)y ] = 4x/3 + 2y/3
so coeff of x in a = coeef of y in B.
More puzzles follow here
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