Hi students, Welcome to **Amans Maths Blogs (AMBIPi)**. Are you looking for * Math Riddles for Adult Questions 21 to 40 with Answer AMBIPi* for brain exercise? In this article, you will get challenging math riddles with answers. Solving these tricky math puzzles are brain exercise and you can do solve these in anytime as you wish.

**Hard Math Riddles 21**: A phonograph record has a total diameter of 12 inches. The recording itself leaves an outer margin of an inch; the diameter of the unused center of the record is 4 inches. There are an average of 90 grooves to the inch. How far does the needle travel when the record is played?

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**Answer: 3 inches**

Explanation: The number of grooves per inch has nothing whatsoever to do with the problem. The needle doesn’t travel around the record; it is the record that turns. The needle is stationary except for its movement toward the center of the disc. That means, it travels 6 – (2 + 1) = 3 inches. Half the diameter less half inner blank plus outer blank.

**Hard Math Puzzles 22**: A greengrocer received a boxful of Brussels sprouts and was furious upon opening the box to find that several had gone bad.

He then counted them up so that he could make a formal complaint and found that 114 were bad, which was 8 per cent of the total contents of the box.

How many sprouts were in the box?

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**Answer: 1425.**

Explanation: 114/8 × 100.

**Math Riddles Hard 23**: Let’s presume there is such an island, not slandered Crete, but one which is inhabited by two tribes, the Atans and the Betans.

The Atans are known all over the world to be inveterate liars, while a Betan always tells the truth. During one stormy night, a ship has run aground near the island. At dawn a man from the ship approaches the island in a rowboat and in the mist sees a group of three men.

Knowing the bad reputation of one of the two tribes he wants to find out which of the two he will have to deal with. So he addresses the first man on the shore and asks him whether he is an Atan or a Betan.

The man’s answer is lost in the roaring of the breakers. However, the man in the boat understands what the second man yells across the surf: “He says he is a Betan. He is one and so am I.”

Then the third man points at the first and yells: “That isn’t true. He is an Atan and I am a Betan.” Now, what is the truth?

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**Answer: **

Explanation: The first man would in any case claim that he is a Betan, even if he is an Atan, because in the latter case he is bound to lie. If the second man confirms the first man’s assertion, it proves that he has told the truth, that is, he himself really is a Betan. If the third man gives the first the lie, it proves that he is a liar, that is, an Atan. Accordingly the first two are Betans, the last an Atan.

**Hard Math Brain Teasers 24**: If seven men can build a house in 15 days, how long will it take 12 men to build a house assuming all men work at the same rate?

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**Answer: 8.75 days. **

Explanation: The seven men take 7 × 15 = 105 man days to build the house. Twelve men can, therefore, build the house in 105/12 = 8:75 days.

**Math Riddles Hard 25**: This is supposed to have happened during an air raid alarm in London during the war. The sirens screamed; all lights go out.

A man jumps out of bed and starts running for the air raid shelter. Then he realizes that it will be cold in the basement and that he had better get a pair of socks. He turns back and opens the drawer which holds his stockings.

Only then is he aware that all the lights are out, which makes it impossible for him to see what he grabs in the drawer. He is a man of self-respect and order and would hate to be seen with two socks of different colors.

He knows that the drawer contains nothing but black and brown socks which, unfortunately, he cannot distinguish in the darkness.

Now, what is the minimum number of socks the man must grab to be sure he will find a matched pair among them when he reaches the shelter?

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**Answer: **

Explanation: Three will be sufficient because that would allow for four possible combinations: three black ones, three brown ones, a black

one and two brown ones, and a brown one and two black ones. All four combinations will allow for one pair of either color, black or brown.

**Hard Brain Teasers 26**: At the end of the day one market stall has eight oranges and 24 apples left. Another market stall has 18 oranges and 12 apples left.

What is the difference between the percentages of oranges left in each market stall?

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**Answer: 35%**

Explanation:

**Hard Math Riddles for Adults 27**: Each of three friends thinks that he is the smartest?

To find out who really is, a fourth friend makes the following suggestion:

He will paint on each of the three men’s foreheads either a black or a white spot without any of the men knowing which color adorns his own brow.

After each man has been marked, all three will be simultaneously led into the same room. Each one who sees a black spot on the forehead of one or two of his friends is supposed to raise his right hand.

The one who finds out first whether he himself is marked black or white and is able to prove his statement will be recognized as the smartest of the three.

The referee now marks each of his three friends with a black spot and lets them enter the room simultaneously. As each of them sees two black spots, all three raise their hands. After a moment’s hesitation one of them states: “I have a black spot.” How did he reason this out?

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**Answer: **

Explanation: This is the way the smartest of the three – let us call him A – reasoned: “If I had a white spot, B would immediately conclude

from the fact that C raised his hand – which in that case could only be attributed to B having a black spot – that he, B himself, was marked with a black spot. Since B didn’t reason that way it is impossible that I have a white spot.”

**Hard Maths Puzzles 28**: Peter is twice as old as Paul was when Peter was as old as Paul is now. The combined ages of Peter and Paul is 56 years. How old are Peter and Paul now? The next two puzzles are of a very similar nature.

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**Answer: Peter 32 and Paul 24**

Explanation: When Peter was 24, Paul was 16 (i.e. half the age Peter is now).

**Math Puzzles Hard 29**: At a party, four people played a game.

Three of them sat one behind the other so that Abe saw Bill and Cal, and Bill saw only Cal who sat in front and saw nobody.

Dave had five hats which he showed to his three friends. Three of the hats were blue, two were red.

Now Dave placed a hat on the head of each of his three friends, putting aside the remaining two hats.

Then he asked Abe what color his hat was. Abe said he couldn’t tell. Bill, asked the color of his own hat, didn’t know for certain either. Cal, however though he couldn’t see any hat at all, gave the right answer when asked what color his hat was.

Do you know what color Cal’s hat was and how he reasoned to find the correct answer?

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**Answer: Four brothers and three sisters..**

Explanation: If Bill and Cal were wearing red hats, Abe would have known that his hat was blue, because there were only two red hats. Since Abe didn’t know the right answer, Cal concluded that there remained only two possibilities for himself and Bill. Either both had blue hats or one had a blue, the other a red hat. If he himself had a red hat, Cal reasoned, Bill would have concluded that he, Bill, had a blue hat, because otherwise Abe would have known that he, Abe, must have a blue hat. So Bill, because he was not able to tell correctly the color of his own hat, involuntarily betrayed to Cal that his hat was not red. Therefore, Cal could tell that his hat was blue.

**Hard Math Riddles for School Students 30**: A bag of potatoes weighs 25 kg divided by a quarter of its weight. How much does the bag of potatoes weigh?

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**Answer: 10 kg**

Explanation: 1/4 of 10 kg = 2.5 and then 25 / 2.5 = 10 kg

**High School Math Puzzles 31**: Six people, let’s call them A, B, C, D, E and F, have witnessed a burglary and are only too willing to let the police know what the burglar-who, by the way, managed to escape looked like.

But you know how eyewitnesses’ accounts go; the descriptions of the criminal differed in every important point, particularly with regard to the color of his hair and eyes, the color of his suit and probable age.

This is the testimony the police got from these six witnesses:

Though these contradictory reports weren’t much help, the police finally got their man and compared his real appearance with the six descriptions.

They found that each of the six witnesses had made three erroneous statements and that each of the four questions had been answered correctly at least once. What did the burglar really look like?

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**Answer: **

Explanation: The problem can only be solved by trial and error, keeping in mind the two stipulations that each witness has made three wrong statements and that each question had been answered correctly at least once. If we assume blond to be the correct hair color, brown, red and black are wrong. Since B and F, like all the witnesses, have answered only one question correctly, the color of the criminal’s eyes cannot be black or brown. It must therefore be blue, which gives one correct answer to both A and D. Consequently, grey, dark blue and “not dark brown” are eliminated as the color of the burglar’s suit, which must be dark brown. Finally, the criminal’s age must be 28 because all other age estimates were made by A, B, C, D and F, who have already one correct answer to their credit. This checks because E’s answers to questions I, II and III are wrong and so his answer to question IV must be correct, as stipulated. By chance, we started with a correct answer (blond for the color of the criminal’s hair). If we start with an incorrect statement we will rapidly strike a snag by finding that fulfillment of the two conditions of the problem becomes impossible. We can, however, start with red for the hair color, and will get another correct solution, namely: eyes, blue; suit, dark blue; age, 28.

**High School Math Brain Teasers 32**: One bag of potatoes weighed 60 kg plus one-quarter of its own weight and the other bag weighed 64 kg plus one-fifth of its own weight. Which is the heavier bag?

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**Answer: Both the same, 80 kg.**

Explanation: 80/4 = 20 and then 20 + 60 = 80

80/5 = 16 and then 16 + 64 = 80.

**High School Math Puzzles 33**: Four men, Jake, Dick, Fred and Eddie, are watchmen in a small factory in Hoboken. Their job consists of two daily shifts of six hours each, interrupted by a rest of several hours.

Two of the men have to be on the job all the time; however, they are not supposed to be relieved at the same time. Each shift has to begin on the hour.

Except for these rules, the four men may agree among themselves on any schedule they want. So they have a meeting at which they ask for the following privileges:

Jake wants to start his first shift at midnight and would like to be off by 4 p.m.

Dick would like to be off from 10 a.m. to 4 p.m.

Fred wants to relieve Dick after the latter’s night shift.

Eddie has to be on the premises at 9 am. to receive special instructions.

After some hours of trial and error the four watchmen finally succeed in making out a shift schedule in accord with the regulations as well as their special wishes. What was this schedule?

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**Answer: **

Explanation: These were the shifts of the four watchmen: Jake from midnight to 6 a.m. and from 10 a.m. to 4 p.m., Dick from 4 a.m. to 10 a.m. and from 4 p.m. to 10 p.m., Fred from 10 p.m. to 4 a.m. and from noon to 6 p.m., and Eddie from 6 a.m. to noon and from 6 p.m. to midnight.

**High School Math Reasoning 34**: An area of land, consisting of the sums of the two squares, is 1000 square metres. The side of one square is 10 metres less than two-thirds of the side of the other square. What are the sides of the two squares?

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**Answer: 10 and 20 metres. **

Explanation: 1000 = 10^{2} + 30^{2} = 100 + 900.

**Best Math Puzzles for Adults 35**: There are communities where the same family names occur time and again.

In one such community it happened that one day there were ten men at the police station, six of them named Miller. Altogether there were six policemen and four burglers.

One Miller had arrested a Miller and one Smith a Smith. However, this burglar, Smith, was not arrested by his own brother.

Nobody remembers who arrested Kelly but anyway, only a Miller or a Smith could have been responsible for that act. What are the names of these ten people?

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**Answer: Twice.**

Explanation: The clues allow us to write down the names (M, S and K) of some of the policemen (p) and burglars (b), as follows:

If we now fill in the names of the last three Millers not yet mentioned – remember, there were six Millers, all told – we will have found out that four policemen were called Miller and two Smith, while two burglars were named Miller, one Smith and one Kelly.

**Math Brain Teasers for Adults 36**: Find four numbers, the sum of which is 45, so that if 2 is added to the first number, 2 is subtracted from the second number, the third number is multiplied by 2 and the fourth number is divided by 2, the four numbers so produced, i.e. the total of the addition, the remainder of the subtraction, the product of the multiplication and the quotient of the division, are all the same.

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**Answer: 6.25 kg.**

Explanation:

**Math Riddles for Adults 37**: Jack gave Jill as many sweets as Jill had started out with. Jill then gave Jack back as many as Jack had left. Jack then gave Jill back as many as Jill had left.

The final exchange meant that poor Jack had none left, and Jill had 80.

How many sweets each did Jack and Jill start out with?

There is a hint to solving this puzzle on page 52.

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**Answer: Jack 50 and Jill 30**

Explanation:

**Math Puzzles for Adults 38**: Brian and Ryan are brothers. Three years ago Brian was seven times as old as Ryan. Two years ago he was four times as old. Last year he was three times as old and in two years time he will be twice as old. How old are Brian and Ryan now?

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**Answer: Brian 10, Ryan 4**

Explanation: