0:00 puzzle 1
1:17 puzzle 2
You will have a gold bar segmented into 7 items.
You have to pay a employee precisely 1 piece of gold per day, day-after-day for 7 days. What’s the fewest variety of cuts of the gold so you’ll be able to pay the employee accurately?
5:41 puzzle 3
7:05 puzzle 4
A household has a number of youngsters. Every boy on this household has as many sisters as brothers however every of the ladies has twice as many brothers as sisters. What number of girls and boys are there?
9:43 puzzle 5
10:41 puzzle 6
If it takes 7 seconds for a clock to strike 7 o’clock, what number of seconds will it take to strike 10 o’clock?
If it takes 7 seconds to listen to 7 ticks of a clock, what number of seconds will it take to listen to 10 ticks?
14:01 puzzle 7
A model of this query was requested as a Goldman Sachs interview query.
There are a lot of hungry lions in a line. A bit of meat is thrown to the entrance.
The primary lion can eat all of the meat or not. However all of the lions know the meat has been cursed. If a lion eats the meat, he’ll flip into the cursed meat for 1 minute. If 1 minute passes, the lion returns and turns into the king. However in the course of the minute, the following lion can select to eat the meat. However the curse continues, and he turns into cursed meat for 1 minute.
A lion may cross and go to the top of the road. If each lion passes on consuming the meat, the meat vanishes.
All of the lions are completely logical. Every desires to eat the meat and be king, however every most prefers to remain alive.
If there are 99 lions in a line, will any lion eat the meat? What if there are 100 lions in line? Or n lions?
As common, watch the video for an answer.
Mind coaching: 7 puzzles to problem your thoughts
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“All might be properly for those who use your thoughts to your selections, and thoughts solely your selections.” Since 2007, I’ve devoted my life to sharing the enjoyment of recreation concept and arithmetic. MindYourDecisions now has over 1,000 free articles with no adverts because of neighborhood assist! Assist out and get early entry to posts with a pledge on Patreon.
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Reply To Mind coaching: 7 puzzles to problem your thoughts
(Just about all posts are transcribed rapidly after I make the movies for them–please let me know if there are any typos/errors and I’ll appropriate them, thanks).
0:00 puzzle 1
There are 10 whole:
–5 vertical (together with 1 in heart)
–4 horizontal
–1 for the 8 in “what number of 8’s”
1:17 puzzle 2
The reply is 2 cuts is minimal.
A single minimize is inadequate, as seen within the 3 doable circumstances:
–Divide into 1 and 6. There isn’t a method to pay 2 items on day 2.
–Divide into 2 and 5. There isn’t a method to pay 1 piece on day 1.
–Divide into 3 and 4. There isn’t a method to pay 1 piece on day 1.
Remarkably solely 2 cuts are wanted. Minimize the gold bar to interrupt it into items of 4, 2, and 1. Then you’ll be able to pay the employee as follows:
Day 1: give 1-piece gold
Day 2: give 2-piece gold, ask for the 1-piece again
Day 3: give the 1-piece gold (whole 3)
Day 4: give the 4-piece and ask for different items again
Day 5: give 1 piece gold (whole 5)
Day 6: give 2-piece gold, ask for 1-piece again
Day 7: give 1 piece (whole 7)
This answer works as a result of the quantities correspond to the binary system place worth system of two2 = 4, 21 = 2, and a pair of0 = 1. The funds could be calculated by utilizing the binary representations of the numbers from 1 to 7, and letting 1 = employee ought to have that piece and 0 = employee mustn’t have that piece.
(4-piece, 2-piece, 1-piece)
Day 1: 001
Day 2: 010
Day 3: 011
Day 4: 100
Day 5: 101
Day 6: 110
Day 7: 111
5:41 puzzle 3
There are 5 e’s within the sentence:
On this circle, “e” is current ______ occasions
In the event you write “5”, nonetheless, then you’ll have 6 e’s within the sentence. However then “six” doesn’t have any e’s so there would solely be 5 e’s within the sentence. The proper reply is to put in writing “seven” which provides 2 extra e’s to the prevailing 5.
7:05 puzzle 4
A household has a number of youngsters. Every boy on this household has as many sisters as brothers however every of the ladies has twice as many brothers as sisters. What number of girls and boys are there?
Let the overall variety of girls and boys be b and g. Every boy has g sisters however solely b – 1 brothers; every lady has b brothers however g – 1 sisters. By the given info:
boy identical sisters as brothers
g = b – 1
lady twice as many brothers as sisters
b = 2(g – 1)
Substituting the second equation into the primary for b provides:
g = 2(g – 1) – 1
g = 2g – 2 – 1
g = 2g – 3
3 = g
Then substituting into the primary equation provides:
3 = b – 1
b = 4
There are 4 boys and three women.
9:43 puzzle 5
10:41 puzzle 6
If it takes 7 seconds for a clock to strike 7 o’clock, what number of seconds will it take to strike 10 o’clock?
If it takes 7 seconds to listen to 7 ticks of a clock, what number of seconds will it take to listen to 10 ticks?
At first look these issues look like the identical. However their solutions are completely different! A strike of a clock is a bell that may final some period of time. Denote a single strike by s– to incorporate the preliminary collision and the strike tone. For 7 o’clock, there might be 7 time intervals:
s–, s–, s–, s–, s–, s–, s–
This takes 7 seconds, so every time interval takes 1 second. Then 10 o’clock would require 10 time intervals, so it would take 10 seconds.
However what about ticks of a clock? Every “tick” is a negligible period of time. Denote a tick by a vertical line | and let — symbolize the practically 1 second between ticks. We will symbolize 7 ticks as:
|–|–|–|–|–|–|–|
Discover that you could hear 7 ticks within the period of time for six time intervals (plus the negligible period of time for the precise tick). So it takes 7 seconds for six time intervals, which means every time interval is 7/6 = 1 + 1/6 seconds.
For 10 ticks we have to add 3 extra time intervals to make 9 time intervals. It will take:
9(7/6) = 63/6 = 10.5 seconds
It takes 10 and a half seconds for 10 ticks, fairly a stunning reply!
14:01 puzzle 7
A model of this query was requested as a Goldman Sachs interview query.
There are a lot of hungry lions in a line. A bit of meat is thrown to the entrance.
The primary lion can eat all of the meat or not. However all of the lions know the meat has been cursed. If a lion eats the meat, he’ll flip into the cursed meat for 1 minute. If 1 minute passes, the lion returns and turns into the king. However in the course of the minute, the following lion can select to eat the meat. However the curse continues, and he turns into cursed meat for 1 minute.
A lion may cross and go to the top of the road. If each lion passes on consuming the meat, the meat vanishes.
All of the lions are completely logical. Every desires to eat the meat and be king, however every most prefers to remain alive.
If there are 99 lions in a line, will any lion eat the meat? What if there are 100 lions in line? Or n lions?
Answer
Take into account smaller circumstances.
n = 1
A single lion will eat the meat, survive the 1 minute, and turn into king.
n = 2
If the primary lion eats the meat, he might be cursed as meat for 1 minute. Throughout this time the second lion can safely eat the meat with out risk of anybody else. So the primary lion can’t eat the meat and passes to the top of the road. However now the second lion faces the identical dilemma: eat the meat to be cursed and the opposite lion can have a free meal. So the second lion should cross. Each lions cross and the meat is just not eaten.
n = 3
If the primary lion eats the meat, the lion is cursed because the meat for 1 minute. Throughout this minute, the state of affairs is an identical to n = 2 during which no lion eats the meat. So the primary lion can safely eat the meat, assured no lion will then eat him as soon as cursed because the meat. The meat is eaten by the primary lion.
n = 4
If the primary lion eats the meat, then the state of affairs is lowered to n = 3 during which the primary lion will eat the meat. So the primary lion can’t eat the meat and can cross. Equally all lions will cross and the meat is just not eaten.
So we now have a sample. If n is odd the meat is safely eaten by the primary lion; in any other case if n is even then no lion eats the meat.
For n = 99 the primary lion eats the meat, and for n = 100 the meat is just not eaten.
References
0:00 puzzle 1
https://www.popsugar.com/tech/how-many-8s-photo-45240276
https://timesofindia.indiatimes.com/life-style/health-fitness/de-stress/optical-illusion-how-many-8s-can-you-spot-in-this-image/articleshow/100931818.cms
1:17 puzzle 2
https://www.enjoymathematics.com/weblog/gold-for-7-days-of-work
5:41 puzzle 3
tailored from
https://www.reddit.com/r/puzzles/feedback/18vgolf/the_vicious_circle/
7:05 puzzle 4
https://testbook.com/question-answer/a-family-has-several-children-each-boy-in-this-fa–5fbf80bbfc893b72de95f225
https://www.wyzant.com/assets/solutions/439319/a_family_has_several_children_each_boy_in_the_family_has_many_sisters_as_brothers_and_each_girl_has_twice_as_many_brothers_as_sisters_how_many_brothers_and_sist
https://aspirestudy.in/notifications/previous_year_papers/nimcet_2016.php
9:43 puzzle 5
https://www.youtube.com/watch?app=desktop&v=QSr4MuPx_2E
10:41 puzzle 6
https://prepyourmathblog.wordpress.com/2016/08/05/some-of-the-puzzles-from-shakuntala-devi-books/
https://en.wikipedia.org/wiki/Shakuntala_Devi
14:01 puzzle 7
tailored from
https://www.efinancialcareers.com/information/the-unusual-riddle-goldman-sachs-might-ask-you-in-a-quant-job-interview
