Thinking questions finishing 1
Answer: Fill the 5l cup with water and pour it into the 3l cup. At this time, the 5l cup contains 2l of water; the 3l cup of water is poured out, and the 2l of water in the 5l cup is poured into the 3l cup. At this time, the remaining 1l of the 3l
cup is full;
Fill up the water, use the 5l cup to fill the 3l cup, then there are 4l of water in the 5l cup.
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One of the four medicine jars has a cloudy medicine jar, and each tablet in the cloudy medicine jar has one gram more than the other three clean medicine jars. How to find the cloudy medicine jar with a scale only once?
Answer: Label the four medicine jars as 1, 2,
3, and 4 respectively; take out 1 pill from No. 1 medicine jar; take 2 pills from No. Take out 4 tablets;
assume that the initial weight of the 10 tablets taken out is 10, and weigh the 10 tablets together;
if the weight is 11, the medicine in No. 1 medicine tank is turbid;
if the weight is 12, the medicine in No. 2 medicine tank is turbid
; If the weight is 13, the medicine in No. 3 medicine tank is turbid;
if the weight is 14, the medicine in No. 4 medicine tank is turbid;
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Four cards with numbers on the front and letters on the back. Now there are four cards on the table, the state is a 1 b 2 Now I want to prove that the opposite of a must be 1 I can only turn over two cards, which two should I turn over?
Answer: If b and 2 are reversed, it can be disproved that the opposite of a must be 1;
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Horse racing problem, 25 horses, 5 tracks, at least how many times can the fastest three horses be selected?
Answer: The 25 horses will be divided into five or five groups, and the bottom two in each group will be eliminated; (five times) the
first place race in the previous competition group with the remaining 15 horses at this time, the group corresponding to the last two after elimination, and the first place in the previous competition group. The third place in the 2nd place group, the second and third place in the 3rd place group; (six times)
There are 6 horses left at this time, the first place in the previous race must be the fastest, and the remaining 5 horses Competition; (seven times)
choose the two fastest horses, plus the first place before, the three horses at this time are the three fastest horses,
so at least 7 times can choose the fastest three horses.
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Five teams of couples go to a party, and each is not allowed to shake hands with his or her spouse, but only with another person at most once. A asked other people and found that the number of handshakes was different for each person, so how many times did A's spouse shake hands?
Answer: There are ten couples in the five teams. Each person shakes hands differently.
If they cannot shake hands with their spouse, the number of handshakes of the ten people is 0, 1, 2, 3, 4, 5, 6,
7, 8 ; person, except for his spouse, the number of handshakes of other people is not 0, and the number of handshakes of his spouse is 0; the
person who shakes hands seven times, except for the person whose number of handshakes is 0, shook hands, and the person who shook hands eight times The person and the rest of the people also shook hands once, and the rest of the people shook hands at least twice, so the number of handshakes for the spouse of the person who shook hands seven times was 1; analogously, the number of handshakes for the spouses of the person who shook hands six times and five times was
respectively 2 and 3;
in the end, the person with the number of handshakes of 4 is left. According to the law, we can know that the number of handshakes of his spouse is also 4.
Since the number of handshakes between A and other people is different, we can know that the person with the number of handshakes is 4 is A. So his spouse has a handshake count of 4.
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You can only carry oil for 60 kilometers, and you can only refuel at the starting point, how to cross the 80 kilometers of desert?
Answer: First take 60 kilometers of oil and go 20 kilometers, then put 20 kilometers of oil at 20 kilometers, and then use 20 kilometers of oil to go back to refuel; the second time to 20 kilometers, put 20 kilometers of oil, and then use 20
kilometers Go back with oil;
when we go to 20 kilometers for the third time and add the 20 kilometers of oil that we put down twice, there are still 60 kilometers of oil left, and we can finish the rest of the road.
Answer: Prepare three such uneven ropes and mark them as 1, 2, and 3 respectively;
light the No. 1 rope from both ends at the same time, and light one end of the No. 2 rope
. After the No. 1 rope is burned, and 30 minutes have passed, light the No. 2 rope At the other end, when the No. 2 rope burned out, 45 minutes had passed; then
immediately ignited both ends of the No. 3 rope, and 1 hour and 15 minutes had passed.
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There are one weight of 7 grams and one weight of 2 grams, and one balance. How to divide 140 grams of salt into 50 grams and 90 grams each by using these items three times?
Answer: Weigh 9g salt with two weights for the first time;
weigh 16g salt with the first salt and 7g weight for the second time; weigh 25g salt with the
25g salt of the first two times for the third time. When there is 50g of salt, the remaining salt is 90g of salt;
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There is a train leaving Los Angeles going straight to New York at a speed of 15 kilometers per hour, and another train traveling from New York to Los Angeles at a speed of 20 kilometers per hour. If there is a bird with a speed of 30 kilometers per hour and two trains starting now, starting from Los Angeles, returning after encountering another car, flying back and forth between the two trains in turn, until the two trains meet on both sides, may I ask, this bird How far did the bird fly?
Answer: The sum of the distance of the two places/the sum of the speed of the two cars = the time for the two cars to meet;
time * bird speed = bird flight distance.
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You have two jars, 50 red pinballs and 50 blue pinballs. A jar is randomly selected, and a pinball is randomly selected to be put into the jar. How to give the red pinball the greatest chance of being selected? What are the exact odds of getting a red ball in your plan?
Answer: Put 1 red ball in the first jar, and put the remaining balls into another jar. The probability at this time is the maximum: 0.5+49/99*0.5≈0.75
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Suppose you have 8 balls and one of them is slightly heavier, but the only way to find out which is which is to compare the two balls on a scale. What is the minimum number of weighings required to find the heavier ball?
Answer: Group 3, 3, and
2 and compare 3 and 3 first. If there is a heavier group in the two groups, randomly select two comparisons from the heavier group. If one is heavier, it is heavier. If the two balls are the same weight, the other ball is heavier.
If the two groups are the same weight, compare the two groups, and the heavier ball is the heavier one.
At least 2 times;
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There are three lights in the room, and three switches outside the room. You can’t see the inside of the room from the outside. You can only enter the door once. How do you distinguish which switch controls which light?
Answer: Turn on a light for a while, then turn off and turn on another light, and enter the house: the
light that is turned on is the second time, the heat is turned on for the first time, and the other is not turned on
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They each bought two pairs of black socks and two pairs of white socks. The fabric quality and size of the eight pairs of socks were exactly the same, and each pair of socks was attached with a label paper. Two blind men accidentally mixed up eight pairs of socks. How can they each get back two pairs of black and white socks?
Answer: Suppose a blind person has x pairs of black socks, then the white socks are y pairs, then another blind person has 4-x pairs of black socks, and 4-y pairs of white socks
; Blind people have (4-x+x)/2 black socks and (4-y+y)/2 white socks respectively.
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There are three baskets of fruit, one basket is full of apples, the second basket is full of oranges, and the third basket is oranges mixed with apples. The labels on the baskets are all deceiving, (that is to say, the labels on the baskets are all wrong) Your task is to take out one of the baskets, take only one fruit from it, and write the labels of the three baskets of fruits correctly.
Answer: Take out a fruit in the box labeled mixed, and label it with what it is;
change the corresponding label to another fruit, and the rest is the mixed box
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60% of a class likes football, 70% likes basketball, and 80% likes volleyball. How much do they like all three kinds of balls?
Answer: 40% don't like football, 30% don't like basketball, and 20% don't like volleyball, then at least 10% of people like three kinds of balls; the most people like all three kinds of balls
is 60%, then 10%-60% I like three balls
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Five chickens can lay five eggs in five days, how many chickens are needed for one hundred eggs in one hundred days?
Answer: Five chickens lay one egg a day, and one hundred eggs in one hundred days require five chickens
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1. A person buys a chicken for 8 yuan, sells it for 9 yuan, buys it back for 10 yuan, and sells it for 11 yuan. How much money does he make?
Answer:
The principle of economics is commodity value, and the pursuit is to maximize profits.
This is the topic of the IBM interview. There are four algorithms:
1. 9-8=1, 11-10=1, 1+1=2, so earn 2 yuan in the end.
2. At first you only have 8 yuan, but in the end you have 11 yuan, so you earn 3 yuan;
3. In the first transaction, the protagonist loses 8 yuan and gains a chicken. In the second transaction, the protagonist gains 9 yuan and loses 1 yuan. chicken; in the third transaction, the protagonist loses 10 yuan and gains a chicken; in the fourth transaction, the protagonist gains 11 yuan and loses a chicken,
so the entire GDP (gross domestic product) produced is 8+9+10+11=38 yuan+4 chickens
4. There are 3 transactions in the whole event, let me see which 3 transactions are?
The first transaction: buy at 8 yuan, sell at 9 yuan, profit 1 yuan; the
second transaction: sell at 9 yuan, buy at 10 yuan, profit -1 yuan; the
third transaction: buy at 10 yuan, 11 yuan The profit of selling for 1 yuan is 1 yuan;
the whole process: 1-1+1=1 yuan
So the analysis shows that this person is a fool, because the last two transactions are worthless
After testing, the company believes that: those
who answer the profit of 2 yuan must be interview failures;
those who answer 3 yuan are even more stupid, because they do not know what the additional cost is, and they must also fail;
those who answer 1 yuan, congratulations, do not belong to The range of fools;
the result is: he could have earned 3 yuan directly, but after his 3 transactions, the total profit has become 1 yuan.
So the correct answer is: -2 yuan!
Those who answer -2 yuan, the interview is successful! ! !
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There is a river in front of Xiao Ming’s house, and the family has to cross the river every night. There is only one lamp and it can only burn for 30 seconds. Only two people are allowed to pass at a time. 8 seconds, grandpa needs 12 seconds, the time to cross the river is calculated according to the slow person, how to cross the river?
Answer: It takes 3 seconds for Xiao Ming and his younger brother to cross the river first;
1 second for Xiao Ming to cross the river to deliver the lamp;
12 seconds for the grandfather and mother to cross
the river; 3 seconds for the younger brother to cross the river to send the lamp
; 6 seconds for Xiao Ming and his father to
cross the river;
Xiao Ming and his younger brother cross the river together, taking 3 seconds
, the total time spent is 29 seconds
Answer: 10 empty bottles for 3 bottles of wine, now there are 4 empty bottles;
4 empty bottles for 1 bottle of wine, now there are 2 empty bottles;
borrow an empty bottle from the boss for 1 bottle of wine and return it to the boss
for 5 bottles liquor
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You get some people to work for you for seven days, and you pay with a gold bar. The gold bars are divided into seven small pieces, and one piece is given out each day. If you can only cut the bar twice, how do you distribute it to these workers?
Answer: Divide the gold bars into 1, 2, and 4 sections .
On the first day, 1 gold nugget is
given to the worker, and the worker has 1 gold nugget at this time;
Give 1 gold nugget on the first day, and the worker has 3 gold nuggets at this time;
give 4 gold nuggets on the fourth day, receive 1, 2 gold nuggets, and the worker has 4 gold nuggets at this time;
give 1 gold nugget on the fifth day, and the worker has 5 gold nuggets at this time Gold nuggets;
on the sixth day, 2 gold nuggets are given and 1 gold nugget is received, and the worker has 6 gold nuggets at this time;
on the seventh day, 1 gold nugget is given, and the worker has 7 gold nuggets at this time.
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Please cut a box of cakes into 8 parts and distribute them to 8 people, but there must still be one part in the cake box.
Answer: The average is 8 yuan, and the one you own is put in the box
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You have a bucket of jelly, there are three types of jelly, yellow, green, and red. Close your eyes and grab two of the same color. How many can you grab to be sure you have two jellies of the same color? (5 seconds - 1 minute)
4
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A fork in the road leads to the honest country and the liar country respectively. Two men came, one known to be from the honest country and the other from the liar country. An honest country will always tell the truth, and a lying country will always tell lies. Now you are going to the country of lies, but don't know which way to go, you need to ask these two people. How should I ask? (20 seconds - 2 minutes)
Answer: Ask "Which way to your country"
Answer: Habitual question + we use decimal numbers
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Give you two 6-faced dice, you can engrave any number from 0-9 on each face, and ask to use them to spell out the date value in any year
Answer: 012345 0126 (9) 78 6 9 shared
Answer: First of all, its area is the largest under the condition of the same material. The second is because if it is square, rectangular or oval, the boring person can pick it up and throw it directly into the underground tunnel! But the round cover can avoid this situation
A: It's not the gas station number that matters, it's how you arrive at that number
Analysis: When this question seems confusing at first, you might want to start by asking how many cars there are in this country. The interviewer might tell you that number, but it's also possible to say, "I don't know, tell me." So, you say to yourself, the population of the United States is 275 million. You can guess that if the average household size (including singles) is 2.5 people, your computer will tell you that there are 110 million households. Do you recall hearing somewhere that the average household owns 1.8 cars, so there are about 198 million cars in the United States. Then, as soon as you figure out how many gas stations are needed to service 198 million cars, you've solved the problem. `
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Imagine you are in front of a mirror. May I ask why the image in the mirror can be reversed left and right, but not up and down?
Answer: Because the image of a person and the person are symmetrical with respect to the mirror, and the mirror is placed upright, so the person in the mirror is upside down, left and right, and upside down, as long as the mirror is placed sideways, the person standing on the mirror is upside down
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For a batch of lights numbered from 1 to 100 with all switches facing up, perform the following operations: Dial the switch once in the opposite direction for multiples of 1, dial the switch again for multiples of 2 in the opposite direction, and dial the switch again for multiples of 3 in the opposite direction. Ask for the number of the lamp that was last turned off.
Answer: Prime numbers are off, others are on
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There are 100 bananas next to a little monkey. It has to walk 50 meters to get home. It can move up to 50 bananas each time, and it has to eat one every time it walks 1 meter. How many bananas can it move home at most? ?
Answer: Let Y be the maximum remaining number of bananas required, and X be the required point (X meters)
1. Y=(100-3X) - (50-X)
2. (100-3X)<=50
is easy to find Out of 3Y=50
x=y=16 and 2/3
First move 50 sticks to 17 meters (point A), eat 17 sticks and leave 33 sticks, leave 16 sticks at point A, bring 17 sticks back to the starting point, eat all 17 sticks, take the other 50 sticks from the starting point to At point A, eat 17 sticks and leave 33 sticks, plus the 16 sticks left at point A, a total of 49 sticks, leaving 50-17=33 meters to the end, 49 eat 33 sticks and leave 16 sticks
problem
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There are 12 balls on a scale, and now we know that only one has a different weight from the others. Ask how to weigh it so that you can find that ball by using it three times. What about 13? (Note that this question does not indicate whether the weight of the ball is light or heavy, so it needs to be carefully considered)
Answer: 4, 4, 4 groups
. Random comparison between two groups. If the weight of the two groups is equal, the other group has abnormal balls. (1)
Divide the other group into two groups, and compare the random group with the normal one. If the weight is equal, The abnormal balls are in the two groups, and vice versa, (2)
Randomly take out one of the two and weigh the normal ones, if they are equal, it is the other one, and vice versa. (3)
Go back to the first step, if the weight of the two groups is not equal (4)
The second step: Take 3 balls from the heavier group and put them aside. Then take 3 from the lighter group and put them in the heavier group. Now the lighter group is left with a ball that may be lighter (not standard) or standard (because it is not known whether the non-standard is lighter or heavier). Take three standard balls and put them on the lighter end. There will be 3 situations, 1, the balance remains the same, 2 is balanced, and 3, the balance is reversed.
The third step is to start with the results of the second step.
If the balance remains the same in the second step, it means that the three balls from the lighter to the heavier ones have the same weight as the three new standard balls, so The non-standard ball is the one left after the lighter group is taken out of three balls and the one left after the lighter group is taken out of three balls. Find one of the two balls and use a standard ball to weigh it.
In the second step, if the balance is balanced, it means that these 8 balls are all standard, and the non-standard ones are the three balls taken out on one side. Because the three balls are taken out on the heavier side, it can be pushed out that the balls with different qualities are heavier. Find a heavier ball among the three balls, and it will come out in one step.
The result of the second step is that if the level of the balance is reversed, the remaining part of the original lighter end is a possibly lighter standard ball, and now the lighter end becomes heavier, indicating that the remaining part is a standard ball. Similarly, the remaining one at the heavier end is also a standard ball. (Because it used to be heavier, but now it is lighter. If it is not standard, then it is heavier than the standard ball, and the balance will not change the other way around.) It means that the non-standard ball gets heavier at the lighter end Among the three balls at one end, because these three balls are at the lighter end, it means that the non-standard ball is lighter than the standard ball. Find a lighter ball among the three balls and just take one step.
As for the case of 13 balls, it is similar to 12 balls. The first grouping is 4, 4, and 5. If 4, 4 are not even, then the calculation is the same as the case of 12 balls. If 4, 4 are tied, the abnormal ball is among the 5 balls. , the way to get it down is to take 3 of these 5 balls and compare them with the three standard balls (the 4 and 4 groups have been determined as standard balls). Find out the light one among the 5 balls, if it is heavy, you can also find the heavy one among these 3 balls for the remaining one, if it is equal, then the abnormal ball is among the remaining 2 of the 5 balls, and the remaining one can be compared It was enough to conclude that it was an anomalous ball.
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During the 24 hours of a day, how many times do the hour, minute and second hands of a clock coincide exactly? What time are they? How did you figure it out?
The minute hand turns 6 degrees per minute,
the hour hand turns 0.5 degrees per minute, and turns 30 degrees per hour
. If they coincide, it means that the hour and minute hands have the same degree to 0 o'clock. Assuming that it is X hour and Y minute, then
Answer: (30 X + 0.5 Y) = (6 Y)
Y=300 X/55
11×2=22 times
1 hour, 13 hours 5 and 5/11 minutes
2 hours, 14 hours 10 and 10/11 minutes
3 hours , 15:16, 4/11,
4:00, 16:21, 9/11,
5:00, 17:27, 3/11,
6:00, 18:32, 8/11,
7:00, 19:38, 2 /11:
08, 20:43, 7/11:
9, 21:49, 1/11,
10, 22:54, 6/11,
12, 24:00
Answer:
Plant trees on an equilateral triangular pyramid-shaped mountain, one tree on the top of the mountain, and the other three
trees are planted on the three points of the bottom of the triangular pyramid. Contact is what you want
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16 coins, A and B take some in turns, and the number taken each time can only be one of 1, 2, and 4. Whoever takes the coin last loses. Q: Does A or B have a strategy that guarantees that they will win?
Answer: 1. Guarantee yourself to win, and leave the last 1 Mei coin to him.
2. Therefore, 1+3 coins should be left for him. Because: if he takes 1, you take 2 and keep 1; if he takes 2, you take 1 and keep 1; if he wants to take 4, you lose.
3. Therefore, 1+3+3 coins should be left for him. Because: if he takes 1, you take 2 and keep 4; if he takes 2, you take 1 and keep 4; if he wants to take 4, you take 2 and keep 1 at once.
4, and so on.
The strategy is to let the opponent take it first, take 3 or 6 coins in each round, and leave the last 1 rose coin to him.
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There are three wine glasses, two of which can hold 8 taels of wine each, and one can hold 3 taels of wine. Now the two big wine glasses are full of wine, how to share the wine evenly among 4 people with only these three glasses?
Answer: The four people are recorded as A, B, C, and D; the amount of alcohol in the three cups is represented by numbers, at first: 880
(1) Start: 880→853, let A drink 3 taels. Change to: 850
(2 ) 850→823, let B drink 2 taels, become: 803.
(3) 803→830→533→560→263→281, let A drink 1 taels (A has finished drinking 4 taels), becomes: 280
(4) 280→253→550→523→820→802→703→730→433→460→163→181, let C and D drink 1 tael each, change to: 080 (5) 080→053→350
→ 323, Let C and D drink 3 taels each, and B drink 2 taels. End
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Draw lots to determine your own number (1, 2, 3, 4, 5). First, No. 1 proposes a distribution plan, and then everyone votes. If and only if more than half of the people agree, the distribution will be made according to his plan, otherwise it will be rejected. Throw it into the sea to feed the sharks. If No. 1 dies, No. 2 will propose a distribution plan, and then the remaining 4 people will vote. If and only if more than half of the people agree, the distribution will be made according to his plan, otherwise it will be thrown away. Enter the sea to feed the sharks and so on, condition: every pirate is a very smart person, can make a rational judgment and make a choice. Question: What kind of allocation plan does the first pirate propose to maximize his own benefits?
Answer: Hypothesis 1: 1 propose a plan (dead) -> 2 propose a plan (dead) -> 3 propose a plan (dead) 4 propose a plan, you will die anyway, because 5 will definitely oppose it, so 4 is to save your life, even if you don’t To distribute diamonds, you must also agree when 3 proposes a plan, or agree when 1 and 2 propose a plan.
Assumption 2: 1, 2 die, 3 will propose a plan 100:0:0 in order to let 4 vote in favor, even if 5 opposes it, it will be invalid.
Assumption 3: 1 is dead, 2 is alive, 2 is deduced, 3 definitely wants him to die, so we can only start with 4, 5, how can 4, 5 agree, and distribute diamonds to them; 98: 0: 1: 1 Assumption 4
: 1 survived, 2 definitely wanted him dead. How he survived, then he must get any two of 3, 4, and 5 to agree. The optimal solution in turn can be 97:0:1:2:0 or 97:0:1:0:2
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A census taker asked a woman, "How many children do you have, and how old are they?" The woman replied: "I have three children, their ages are multiplied to 36, and the sum of ages is equal to the house number of the isolated room." Census The enumerator immediately went to the next door, looked at 13, and came back and said: “How much more information do I need.” The woman replied: “I am very busy now, and my oldest child is sleeping upstairs.” The enumerator said: “Thank you, I already know the question: What are the ages of those three children?
Analysis, let the ages of three people form a combination of natural numbers (x, y, z), a total of three conditions,
condition 1: multiply the ages of the three people to 36; choose a combination that satisfies xyz=36;
condition 2: know the ages of the three people After summing up, their ages still cannot be determined; from the combination above, find out that the sum of xyz has the same
combination;
only (9,2,2)=13, (6,6,1)=13
condition three : One of the three children is older than the other two. The eligible combinations are only (9, 2, 2)