Can anyone solve this tricky math problem

Christmas puzzle

Santa's elves want to give their boss a present this year. In addition, they thought that they would cook the old woman's favorite dish: reindeer pigeon eggs. Unfortunately, they have a little problem there. Reindeer pigeon eggs are very delicate. They are only edible if they are cooked for exactly 45 seconds. Unfortunately, the elves couldn't find a clock or any other timepiece. Instead, one of them found only two fuses, which he knows will burn for exactly one minute each. The elves were happy because that way it was possible to measure the time.
How could the elves measure 45 seconds?
(If you know the answer, e-mail to servant Stephan)

Santa Claus says to Rudolph: "If I multiply the age of 3 of my pixies, I get 36. If I add them, I get the number of balls on my Christmas tree. Do you now know how old the 3 pixies are?" Rudolph immediately goes to count the balls on the Christmas tree, but then comes back very sad: "I can't say how old you are yet." Santa Claus replied: "But you know that the oldest of my elves always feeds you and your comrades." Now Rudolph could solve the riddle.
How old are Santa's elves?
(If you know the answer, e-mail to servant Stephan)

Santa Claus is a sought-after employer with snowmen; work in winter, "laze in the sun" the rest of the year. But if you want to work for Santa Claus, you have to be a role model for children, i.e. also good at school. That is why performance assessments take place regularly. Today one in math, it's about divisibility.

Santa Claus writes a natural number x between 1 and 50,000 on the board.

  • The first snowman finds that x is divisible by 2.
  • The second snowman finds that x is divisible by 3.

  •     ...
  • The twelfth snowman finds that x is divisible by 13.

  • Unfortunately, two of the snowmen miscalculated and gave a wrong answer; and both directly one after the other.

    What number did Santa Claus write on the board?
    (If you know the answer, e-mail to servant Stephan)

    Santa Claus says to Knecht Ruprecht: "If I multiply the age of 3 of my reindeer, I get 2450. If I add it, I get the height of the Christmas tree in front of my hut. Now tell me how old the 3 reindeer are!" After Knecht Ruprecht had measured the height of the Christmas tree, he came to Santa Claus: "Hmmm, I can't tell you the solution!" He replied: "I completely forgot to say that the oldest of my reindeer is still younger than me." Knecht Ruprecht immediately knew the right solution.
    How old is Santa Claus now?
    (If you know the answer, email Servant Stephan)

    After the elves have made or bought the presents, they now have to wrap a huge number of presents for Christmas. This is extremely boring work, so that the elves pass the time with numbers. In doing so, they discover something amazing:
    The number of Christmas presents that the elves are supposed to wrap is a 10-digit number in which every digit from 0 to 9 occurs exactly once. And if you only take the first n digits of the number, the resulting number is always divisible by n without a remainder. And that even applies to all n from 1 to 10!
    How many Christmas presents do the elves have to pack?
    (If you know the answer, email Servant Stephan)

    One day before Christmas, Santa Claus wants to rest for the backbreaking job the next day. But what is it, loud music resounds from the reindeer quarters! Don't they have anything better to do today?
    Santa quickly runs over and removes anything that looks like musical instruments. In order to keep his reindeer happy anyway, Santa Claus gives them the following self-referential sentence to puzzle over. That should keep them busy until tomorrow.

    Only the fool would take trouble to verify that his sentence was composed of ten a s, three b s, four c s, four d s, forty-six e s, sixteen f s, four g s , thirteen h s, __________ i s, two k s, nine l s, four m s, twenty-five n s, __________ o s, five p s, sixteen r s, forty- one s s, thirty-seven t s, ten u s, eight v s, __________ w s, four x s, eleven y s, twenty-seven commas, twenty-three apostrophes, seven hyphens and , last but not least, a single!

    Which three numerical values ​​(in English) have to be in the gaps so that the sentence can fulfill itself?
    (If you know the answer, email Servant Stephan)

    Eternal competition between the Easter Bunny and Santa Claus. This time the Easter Bunny seems to win. He has captured Santa Claus and now wants to throw him to the lions to eat. But he gives the poor old man one last chance:
    The room where Santa Claus is has two doors. One leads to freedom, the other directly to the lion cage. There is a guard in front of every door. One always tells the truth while the other always lies. Santa knows that; but he neither knows which door leads where, nor which guard is telling the truth. He only gets the chance to ask one of the guards a single question in order to be released.
    What question does Santa Claus have to ask?
    (If you know the answer, email Servant Stephan)

    Once upon a time, a long, long time ago, on a cold winter night after Christmas. Santa Claus prepared a liter of delicious mulled wine for his seven reindeer, because they had to pull the sleigh all night and were totally knocked out.
    After Santa Claus had filled the seven jugs, Rudolf, the first reindeer, remembered that it had to steer the sleigh again later and was therefore not allowed to drink alcohol. He divided his ration of mulled wine into six equal parts and poured them into the jugs of the other six reindeer. But Dancer didn't want mulled wine either, because it was too hot for him. He also divided his ration into six equal parts and then distributed them to the other six (unfortunately also to Rudolf ...).
    So it went on until the seventh reindeer. One had just swallowed an aspirin beforehand, the other was fresh from rehab: that evening every reindeer had a reason why it didn't want to drink and distributed its ration to the others.
    After the seventh reindeer had also distributed his ration, Santa Claus remarked with astonishment: "Now each of you has exactly the same amount of mulled wine that I initially served!".
    How much mulled wine did Santa Claus give each reindeer?
    (If you know the answer, e-mail to servant Stephan)

    Santa Claus wants to reward his 12 reindeer for their loyal service. Everyone should receive a gift from him. 11 gifts are the same, only Rudolph receives a special gift because, as the leader, he always has the greatest responsibility. He asks his elves to wrap the presents in a festive way and to mark the present for Rudolph so that there are no mix-ups.
    Yes, oh dear, when Santa Claus comes back, there are 12 identical-looking packages.


    And the reindeer are about to come. Santa Claus has an idea. He quickly fetches his old beam balance (one with a lever that can be swiveled in the middle and one weighing pan each on the left and right) and weighs out the parcels. After all, 11 packages are equally heavy, only one is lighter or heavier than the others. Unfortunately, Santa Claus cannot remember (probably due to his age) whether Rudi's present is lighter or heavier than the others.

    How can Santa Claus find out which package is for Rudolph with as little weight as possible? What is the minimum number of weighs that is required for this?

    (If you know the answer, email Servant Stephan)

    Not everything that Santa Claus gives the children can not be made by his elves in the elf factory. So every now and then he sends her to go shopping. This time too he sends her out to get four smaller things. When the elves come back from shopping, Santa Claus asks what the four items cost. One of the elves, a little rogue, allows himself a joke and says: "The prices of the 4 things add up to exactly 9.27 . But when multiplied they also add up to exactly 9.27 ."

    What are the four prizes?
    (If you know the answer, e-mail to servant Stephan)

    An expedition goes to visit Santa Claus at the North Pole. Your tracked vehicle consumes 1 liter of mulled wine diesel per kilometer and has a tank that holds exactly 1000 liters of mulled wine diesel. The base camp is located exactly 2000 kilometers from the North Pole and has unlimited supplies of mulled wine diesel. On the way, the expedition can create storage tanks of any size.
    Tip for the way back: Santa Claus also has an infinitely large supply of mulled wine diesel.

    How many liters of mulled wine diesel are required at least
    to get from base camp to the North Pole?
    (If you know the answer, email Servant Stephan)

    It is well known that Santa Claus and Knecht Ruprecht are seasonal workers; they work at Christmas and have the rest of the year off. (If you disregard the production of the presents, that's what the gnomes are for.) But what do the two of them do all year round so as not to die of boredom? Of course, they solve tricky math problems! The last of these looked like this:

    Two numbers (not necessarily different) are selected from the natural numbers greater than 1 and not greater than 100. Only the sum of the two numbers is given to the servant Ruprecht, only the product is given to Santa Claus. On the phone, Knecht Ruprecht says to Santa Claus: "I don't see any way you can calculate my sum." An hour later, Santa Claus calls him and says: "I know your sum." And a little later Knecht Ruprecht calls him back to report: "Now I know your product!"

    What are the two numbers?
    (If you know the answer, email Servant Stephan)

    after Christmas, which is why they have a snowball fight every now and then.

    In order to keep them busy, Santa Claus gives you the following tricky puzzle:

    Rudolph, Dancer and Comet are supposed to find out two numbers. To do this, you receive the following information: Both numbers are in the range from 1 to 1000, and both are integers (i.e. no point numbers), and it is also possible that both numbers are identical. Rudolph also finds out the product of the two numbers, Dancer gets the sum and Comet the difference. This leads to the following conversation:

    Rudolph:I don't know the numbers.
    Dancer:You don't need to tell me because I already knew that.
    Rudolph:Then I know the numbers now.
    Dancer:I know her now too.
    Comet:I don't know the two numbers yet. I can only guess one number that is probably there, but I don't know for sure.
    Rudolph:I know what number you're guessing, but it's wrong.
    Comet:OK, then I know both numbers now.
    What are the two numbers?
    (If you know the answer, email Servant Stephan)
    (PS: Don't expect a solution, because I don't have one myself yet.)