Interview Trap Riddle: Hungry Worm & Old Tree
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Date: 2023-11-15
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Comments and reviews: 29
Devon
Answer = day 30. On the last day, it will eat half of the leaves. On day 30th it will eat 2-29 of the leaves, but the total the worms will eat will be, 2-29 + 2-29- 1 leaf. Therefore the day before the last, the total leaves will be 2-29 - 1, and so half of this will be 2-29 - 0. 5 leaves, which is greater than 2-29 -1. So the worm will eat half of the leaves on DAY 30
This is because the sum of integers doubling is equal to twice the last integer minus 1 or 2-n +1 - 1. so take 1 + 2 + 4 this total is 7 or it is 8 -1 but 8 is n+ 1 - 1. Or one could look at it as 1 + 2 +4 is 4 + 4-1 = 7 half of this is 3. 5 here 4 is greater than 3. 5 but 4-1 is less than 3. 5, therefore, half of 7 can only be obtained from the 4 (so the case of the worm the last day). Answer last day or day 30
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Answer = day 30. On the last day, it will eat half of the leaves. On day 30th it will eat 2-29 of the leaves, but the total the worms will eat will be, 2-29 + 2-29- 1 leaf. Therefore the day before the last, the total leaves will be 2-29 - 1, and so half of this will be 2-29 - 0. 5 leaves, which is greater than 2-29 -1. So the worm will eat half of the leaves on DAY 30
This is because the sum of integers doubling is equal to twice the last integer minus 1 or 2-n +1 - 1. so take 1 + 2 + 4 this total is 7 or it is 8 -1 but 8 is n+ 1 - 1. Or one could look at it as 1 + 2 +4 is 4 + 4-1 = 7 half of this is 3. 5 here 4 is greater than 3. 5 but 4-1 is less than 3. 5, therefore, half of 7 can only be obtained from the 4 (so the case of the worm the last day). Answer last day or day 30
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chinareds54
Was too lazy to do the actual maths, so I just used a spreadsheet to calculate the number of leaves eaten per day and the total number eaten. 1, 073, 741, 823 total leaves are eaten, and 536, 870, 911 leaves are eaten by the end of day 29. 1, 073, 741, 823/2 = 536, 870, 911. 5, so exactly half the total leaves are eaten when the worm eats the first half leaf on day 30. After brute forcing the solution, I went and considered the maths for a bit. On day n, the worm eats 2-(n-1) leaves, and the total number of leaves eaten is (2-n)-1. Half of this total is (2-(n-1)-0. 5 So this means that EVERY day, the worm eats exactly half of the cumulative total after he eats the first half leaf of the day. Day 1: 0. 5 = 1/2. Day 2: 1. 5 = 3/2. Day 3: 3. 5 = 7/2. etc.
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Was too lazy to do the actual maths, so I just used a spreadsheet to calculate the number of leaves eaten per day and the total number eaten. 1, 073, 741, 823 total leaves are eaten, and 536, 870, 911 leaves are eaten by the end of day 29. 1, 073, 741, 823/2 = 536, 870, 911. 5, so exactly half the total leaves are eaten when the worm eats the first half leaf on day 30. After brute forcing the solution, I went and considered the maths for a bit. On day n, the worm eats 2-(n-1) leaves, and the total number of leaves eaten is (2-n)-1. Half of this total is (2-(n-1)-0. 5 So this means that EVERY day, the worm eats exactly half of the cumulative total after he eats the first half leaf of the day. Day 1: 0. 5 = 1/2. Day 2: 1. 5 = 3/2. Day 3: 3. 5 = 7/2. etc.
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Lexx-o-
In the lotus problem, we are asked to find value of the progression element, and the main thing there is to understand what element the questioner needs. In the worm problem, we need to find half the sum of a limited progression and compare it with the elements of the progression. The main difference between these problems is that they ask you to find different things - you should not compare them)
The problem with the worm requires some calculations that not everyone can do in 5 seconds. Limited time requires immediate action, and if a person knows about the lotus problem, then he will draw a false analogy and give wrong answer, since he will not have time to test his theory.
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In the lotus problem, we are asked to find value of the progression element, and the main thing there is to understand what element the questioner needs. In the worm problem, we need to find half the sum of a limited progression and compare it with the elements of the progression. The main difference between these problems is that they ask you to find different things - you should not compare them)
The problem with the worm requires some calculations that not everyone can do in 5 seconds. Limited time requires immediate action, and if a person knows about the lotus problem, then he will draw a false analogy and give wrong answer, since he will not have time to test his theory.
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Devon
On the last day, the worms ate 536, 870, 912 leaves ( or 2-29. On all the days up to the last day, the worms ate 536, 870, 911 leaves (or 2-29-1, so total leaves worms ate was 1, 073, 741, 823 or 2-29 +2-29-1, and half of that is 536870911. 5 (or 2-29 - 0. 5. So you can see that the worms completed 536, 870, 911. 5 leaves (or 2-29-0. 5)or HALF of it, on the LAST DAY or Day 30 given that 2-29-0. 5 (or Half) is GREATER THAN 2-29- 1, which is all the leaves eaten PRIOR TO the last day.
So on day 30th (or the last day) the worm completed half of all the leaves in the first second of the day since would only need to eat 0. 5 leaf on day 30th to reach half of 2-29 +2-29-1
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On the last day, the worms ate 536, 870, 912 leaves ( or 2-29. On all the days up to the last day, the worms ate 536, 870, 911 leaves (or 2-29-1, so total leaves worms ate was 1, 073, 741, 823 or 2-29 +2-29-1, and half of that is 536870911. 5 (or 2-29 - 0. 5. So you can see that the worms completed 536, 870, 911. 5 leaves (or 2-29-0. 5)or HALF of it, on the LAST DAY or Day 30 given that 2-29-0. 5 (or Half) is GREATER THAN 2-29- 1, which is all the leaves eaten PRIOR TO the last day.
So on day 30th (or the last day) the worm completed half of all the leaves in the first second of the day since would only need to eat 0. 5 leaf on day 30th to reach half of 2-29 +2-29-1
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Andras
In case of the pond, it happens south of the equator so the coriolis force will cause the process to end sooner. In the case of the worm, it has to overcome the coriolis force of the northern hemisphere so it can only reach half on the last day. If we had a slightly weaker strong nuclear force then they would be equal. It can also be checked with the Pythagorean theorem because the partial pressure at eye level is not significant in relation to the annual number of sunny days in the vicinity of storm clouds.
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In case of the pond, it happens south of the equator so the coriolis force will cause the process to end sooner. In the case of the worm, it has to overcome the coriolis force of the northern hemisphere so it can only reach half on the last day. If we had a slightly weaker strong nuclear force then they would be equal. It can also be checked with the Pythagorean theorem because the partial pressure at eye level is not significant in relation to the annual number of sunny days in the vicinity of storm clouds.
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Devon
I think this is another logical way to look at this problem. Since the total leaves, the worm will eat will be 2-n + 2-n-1, in which 2-n is what the worm will eat on the last day (it doesn't matter what the last day is ) then 2-n -0. 5 ( or 2-n + 2-n-1 divided by 2) is HALF the leaves, the worm will eat. But since 2-n is greater than 2-n-1, but half is 2-n - 0. 5, the worm will have to wait until the last day to complete 2-n - 0. 5. so the answer is the last day, and this how I did it below. So day 30.
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I think this is another logical way to look at this problem. Since the total leaves, the worm will eat will be 2-n + 2-n-1, in which 2-n is what the worm will eat on the last day (it doesn't matter what the last day is ) then 2-n -0. 5 ( or 2-n + 2-n-1 divided by 2) is HALF the leaves, the worm will eat. But since 2-n is greater than 2-n-1, but half is 2-n - 0. 5, the worm will have to wait until the last day to complete 2-n - 0. 5. so the answer is the last day, and this how I did it below. So day 30.
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Mycroft616
I got Day 30, but my method was quite different.
Basically 2-0 + 2-1 + 2-2 + 2-3 +. + 2-n can be simplified as 2-(n + 1) - 1. Knowing this, on Day 30, the worm ate 2-29 leaves that day and 2-30 - 1 over all 30 days. We can easily prove that (2-29)/(2-30) = 0. 5. We can also easily prove that 1/n < 1/(n - 1. Therefore, we know that (2-29)/(2-30 - 1) must be greater than 0. 5. Since the worm ate more than half of the leaves on Day 30, the halfway point must have been crossed on Day 30.
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I got Day 30, but my method was quite different.
Basically 2-0 + 2-1 + 2-2 + 2-3 +. + 2-n can be simplified as 2-(n + 1) - 1. Knowing this, on Day 30, the worm ate 2-29 leaves that day and 2-30 - 1 over all 30 days. We can easily prove that (2-29)/(2-30) = 0. 5. We can also easily prove that 1/n < 1/(n - 1. Therefore, we know that (2-29)/(2-30 - 1) must be greater than 0. 5. Since the worm ate more than half of the leaves on Day 30, the halfway point must have been crossed on Day 30.
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Jagdish
I have a doubt in the explanation given as this one has cumulative result while lotus one is not cumulative.
In the lotus problem there are total
1 lotus on day 1
2 on day 2
4 on day 3
And so on.
And in worm riddle there are total
1 leaf eaten on day 1
3 till day 2
7 till day 3
And so on. So, here #leaves eaten are cumulative result. And total leaves eaten till day 30 is 2-30 -1 and half of which is 2-29 -0. 5 > 2-29 -1(till day 29) so answer is 30.
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I have a doubt in the explanation given as this one has cumulative result while lotus one is not cumulative.
In the lotus problem there are total
1 lotus on day 1
2 on day 2
4 on day 3
And so on.
And in worm riddle there are total
1 leaf eaten on day 1
3 till day 2
7 till day 3
And so on. So, here #leaves eaten are cumulative result. And total leaves eaten till day 30 is 2-30 -1 and half of which is 2-29 -0. 5 > 2-29 -1(till day 29) so answer is 30.
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Thunderbear69
Your answer is only true if there are enough leaves left for the last day. If we take the 4 day example, suppose the tree has 12 leaves, there would only be 5 leaves left on the last day and therefore the penultimate day would be the correct answer. In fact, the ONLY scenario where your answer is the right one is when the tree has exactly 15 leaves, if it has between 8 and 14 your answer is incorrect, which statistically means you are only correct in one case out of eight.
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Your answer is only true if there are enough leaves left for the last day. If we take the 4 day example, suppose the tree has 12 leaves, there would only be 5 leaves left on the last day and therefore the penultimate day would be the correct answer. In fact, the ONLY scenario where your answer is the right one is when the tree has exactly 15 leaves, if it has between 8 and 14 your answer is incorrect, which statistically means you are only correct in one case out of eight.
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Stefano
If it keeps on eating like that, on the 30th day it must eat 536, 870, 912 leaves. If it needs even ONE second to eat a single leaf, it will need around 17 YEARS to eat that many leaves. No insect can eat at that pace so 17 years is very very generous and the answer must be hundreds of years. I know that is NOT the point, but you could make it with another example a little more plausible. Not a good riddle.
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If it keeps on eating like that, on the 30th day it must eat 536, 870, 912 leaves. If it needs even ONE second to eat a single leaf, it will need around 17 YEARS to eat that many leaves. No insect can eat at that pace so 17 years is very very generous and the answer must be hundreds of years. I know that is NOT the point, but you could make it with another example a little more plausible. Not a good riddle.
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mohammed
Nice riddle, however I am not satisfied with the comparison between the two riddles.
In lotus riddle if you'd have asked that on which day the lotus increased its size by the half size of the pond, the answer would be 30th day same as the warm riddle which says on which day the warm eat exactly half number of leaves.
I don't think initial size matters here
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Nice riddle, however I am not satisfied with the comparison between the two riddles.
In lotus riddle if you'd have asked that on which day the lotus increased its size by the half size of the pond, the answer would be 30th day same as the warm riddle which says on which day the warm eat exactly half number of leaves.
I don't think initial size matters here
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MANIKANDAN
Worm puzzle is ok but the lotus puzzle is confusing me. You it has a initial state say length (1cm) then day 1 it doubles (2 cm) then day 2 (4 cm) then day 3(8 cm) and day 4(16 cm. Consider day 4 i final day means the total size is 31 cm (including initial state. The half of size is 15. 5 will comes in day 4. Please clarify me clearly ASAP.
Thanks
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Worm puzzle is ok but the lotus puzzle is confusing me. You it has a initial state say length (1cm) then day 1 it doubles (2 cm) then day 2 (4 cm) then day 3(8 cm) and day 4(16 cm. Consider day 4 i final day means the total size is 31 cm (including initial state. The half of size is 15. 5 will comes in day 4. Please clarify me clearly ASAP.
Thanks
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Byron
Your logic for the lotus pond is flawed. The initial size and the day 1 size are the same item and you count them as separate data points. However, the questions are different. The lotus flower asks for the ratio of the last two days and the worm asks for the ratio of the last day to the total (or everything BUT the last day to the total.
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Your logic for the lotus pond is flawed. The initial size and the day 1 size are the same item and you count them as separate data points. However, the questions are different. The lotus flower asks for the ratio of the last two days and the worm asks for the ratio of the last day to the total (or everything BUT the last day to the total.
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mat
Very nice problem howerver your explanation of the difference with the lotus in the pond riddle is false: the point is not that the lotus has an initial lenght, the point is that his lenght is equal to 2-n on the day n. The amount of leaves eaten is equal to 2-0 + 2-1 +. + 2-n on day n. Thats why these two problems are different
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Very nice problem howerver your explanation of the difference with the lotus in the pond riddle is false: the point is not that the lotus has an initial lenght, the point is that his lenght is equal to 2-n on the day n. The amount of leaves eaten is equal to 2-0 + 2-1 +. + 2-n on day n. Thats why these two problems are different
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mat
Very nice problem howerver your explanation of the difference with the lotus in the pond riddle is false: the point is not that the lotus has an initial lenght, the point is that his lenght is equal to 2-n on the day n. The amount of leaves eaten is equal to 2-0 + 2-1 +. + 2-n on day n. Thats why these two problems are different
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Very nice problem howerver your explanation of the difference with the lotus in the pond riddle is false: the point is not that the lotus has an initial lenght, the point is that his lenght is equal to 2-n on the day n. The amount of leaves eaten is equal to 2-0 + 2-1 +. + 2-n on day n. Thats why these two problems are different
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Amlan
The only difference between the two are. in case of lotus its size increases TO double. and in case of worm the nos of leaves eaten increases BY double.
That's why in case of worm we need to take the sum of gp series in account while in case of lotus we need to consider only the terms of the series
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The only difference between the two are. in case of lotus its size increases TO double. and in case of worm the nos of leaves eaten increases BY double.
That's why in case of worm we need to take the sum of gp series in account while in case of lotus we need to consider only the terms of the series
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Nature
I think that your explanation is quite wrong, it is better that if you answered if even number of leaves
are present then answer is ' the day before the last day ' and if odd number of leaves are present then answer is ' last day '.
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I think that your explanation is quite wrong, it is better that if you answered if even number of leaves
are present then answer is ' the day before the last day ' and if odd number of leaves are present then answer is ' last day '.
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Anil
You have an OCD if you do not know that 7. 5 is good enough for 7 or 8. If you would give too much of weightage to things being 'exact', you would not be able to use dettol, because that also kills only 99. 9% of germs.
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You have an OCD if you do not know that 7. 5 is good enough for 7 or 8. If you would give too much of weightage to things being 'exact', you would not be able to use dettol, because that also kills only 99. 9% of germs.
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Ashish
Little bit confused with complicated explanation towards the end and comparison between puzzles. Simply what you need to assess is whether problem needs cumulative sum or not. This one does and other pond one doesn-t.
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Little bit confused with complicated explanation towards the end and comparison between puzzles. Simply what you need to assess is whether problem needs cumulative sum or not. This one does and other pond one doesn-t.
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Palash
it is different from river problem because in river problem we doubles all the initial amounts like
day 3=2 times of 1+2
but here we only doubles it's initial amount
day 3=2-day2
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it is different from river problem because in river problem we doubles all the initial amounts like
day 3=2 times of 1+2
but here we only doubles it's initial amount
day 3=2-day2
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Indrojit
Lotus: Doubles its total number. that it don't only consider previous day but sum of all previous days.
Worm: Consider only previous day. so for half we need to add all days
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Lotus: Doubles its total number. that it don't only consider previous day but sum of all previous days.
Worm: Consider only previous day. so for half we need to add all days
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Christian
Under the assumption that the worm will use the same rule or pattern to eat all the leaves, if he eats the total of leaves on day 30, then he ate the half on day 29.
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Under the assumption that the worm will use the same rule or pattern to eat all the leaves, if he eats the total of leaves on day 30, then he ate the half on day 29.
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Bhavesh
The correct explanation would be in lotus riddle we are asked to find n of a tn for given GP while in worm riddle we are asked to find n of Sn for given GP
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The correct explanation would be in lotus riddle we are asked to find n of a tn for given GP while in worm riddle we are asked to find n of Sn for given GP
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Jay
This presupposes that in those 30 days, no leaves grow back. I was assuming it would only take a day to regrow an eaten leaf, so it wouldn't be cumulative.
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This presupposes that in those 30 days, no leaves grow back. I was assuming it would only take a day to regrow an eaten leaf, so it wouldn't be cumulative.
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Vishal
You are right. I got successfully trapped in Lotus puzzle. but the best thing is that you compared both puzzles at last and cleared my confusion.
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You are right. I got successfully trapped in Lotus puzzle. but the best thing is that you compared both puzzles at last and cleared my confusion.
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MyKazam
Oh but there is one more trick, if you said 30, you have been trapped again, the answer is -no day- because that-s not a worm, it-s a lady bug.
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Oh but there is one more trick, if you said 30, you have been trapped again, the answer is -no day- because that-s not a worm, it-s a lady bug.
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Shuvam
My answer was log(536, 870, 912. 5) with base 2. and you know how that was calculated --
Pls tell me which country are you from?
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My answer was log(536, 870, 912. 5) with base 2. and you know how that was calculated --
Pls tell me which country are you from?
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Nirupam
Total leaves = 1 + 2 + 4 +. + 2-29
= (2-30 - 1)/(2 - 1) = 2-30 - 1 = odd number of leaves
Half leaves in 30 days
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Total leaves = 1 + 2 + 4 +. + 2-29
= (2-30 - 1)/(2 - 1) = 2-30 - 1 = odd number of leaves
Half leaves in 30 days
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charles
dam, totally fell in the trap. i should have thought about it abit longer. knowing your riddles are never that simple
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dam, totally fell in the trap. i should have thought about it abit longer. knowing your riddles are never that simple
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