MAth New Drill (Level 2) : Logical Reasoning - Take stones with two players

There is a game that two players take some stones out of 33 stones in turn and the person who takes a stone remained at the end is defeated. 

The number of stones can be taken at a time is three or less one or more. 

Do you choose the first mover or second?

Math New Drill (Level 2) : Logical Reasoning Find numbers

A～I expresses the number of either 1-9. 

The result of calculation shows as above. Find each number.

Math New Drill (Quiz) : Floral fortune-telling

There is a flower with 13 petals as shown in the figure below.



2 people decide an order to take petal.

One petal or two petals adjacent for once are taken in turn.

There is a legend that fortune visits for the person who takes the last petal.

When you do this floral fortune-telling with somebody, do you choose the first taker or the second taker in your turn?

New Math Drill : Level 2 : Logical Reasoning Problem5 JOHOKUSAITAMA-2014

As shown in the figure, five circles cross and have nine parts. 

Number from 1 to 9 are in the nine parts one by one. 

The sum of numbers in each circle becomes all 11.

(1) Find the sum of four numbers in P, Q, R and S.

(2) Find numbers in nine parts. 

Noted that the number in Q is smaller than the number in R.

Math New Drill : Level 2 SNS00-1201-L2 Cards 0f 1 ~5 delivered to 5 persons

I distributed each card on which 1 -5 was written to 5 people of A, B, C, D, E and questioned in turn. 

5 people heard other persons' questions and answered. 

I asked A who had the biggest card, but A did not understand. 

I asked B whether B had a number bigger than C, but B did not understand. 

I asked C whether C had a number bigger than D, but C did not understand. 

I asked D whether D had a number bigger than B, but D did not understand. 

I asked B again whether B had a number bigger than C, then B said B did not have a number bigger than C. 

Answer the number on the card each person has.

Math New Drill : SNS00-1201-L1

Two persons among Taro, Jiro and Hanako have dog and two persons have cat. 
There is no one who has neither dog nor cat. 
Those who have the dog are liar. 
It cannot be said that the person who does not have dog is a honest person. 
Taro said "Jiro has cat." 
Jiro said "Hanako has cat." 
What do they have, respectively? 

Math Problem : LLL.3 Volleyball tournament of five teams

In a volleyball tournament the league match (round-robin matches) of 5 teams, A, B, C, D, and E is held.
There is one court and the schedule is for two days.
The game of this tournament is organized in accordance with the following administration rules.
<Rule 1>
In addition to two teams under game, there are one team that referee a game and two teams that are waiting to play a next game.
<Rule 2>
There are five games held a day.
<Rule 3>
One team does not hold two games continuously among one day. One team may hold the 5th game on Day1 and the first game on Day2.
<Rule 4>
Each team will referee a game one time with the 1st day on the 2nd, respectively.
A part of schedule organized according to this rule is presented as it is shown in the next table.
Fill in all blanks in the table for answer. 

Math Problem : LLL.2 Find the road to paradise

While wandering about the wilderness without any water and food and it had been utterly ruined, there are right and left roads toward hell or paradise and JIZO (the guardian deity of children) was standing there.
The way of reply of JIZO to your inquiry is only shaking or nodding its head and moreover, it is not understood that it is a liar JIZO or a honest JIZO.
What is the right inquiry to find the road to paradise by only once?

Math Problem : LLL.1 Find the way to go

I come to the fork in the road you do not know which way to go to A town, either way to B town.
There are two persons, one is Taro who always tell or do the truth and another is Jiro who always say or do the contrary to the truth.
I do not know which person is Taro.
Find out the question I can find the way to A town asking the question only to one of two persons.

Math Problem : LL.17 Seats of six persons

Six persons, A, B, C, D, E, and F, sat down groups of three face to face as shown in the figure.
These six persons explained how to sit down as follows.

A : I sat on the edge.
B : A was on the right hand side of the front looked at from me.
C : I sat on the front of E.
D : F was sitting on the left edge of the opposite side looked at from me.
E : C was sitting on the same side as F.
F : I and B were not facing each other.

Write the seat of A to F in a figure.

Math Problem : LL.16 Rabbits in the hut

In a certain zoo, rabbits are kept in the hut which looks like the form as shown in Fig. 1 when it is seen from right above. 

In the inside of the hut, there are transparent boards at the position of the dotted line in the figure and it is divided into eight rooms. 

The shadow portion in the middle is not a room. 

There are four windows in the hut and we can see rabbits by looking through the windows. 

For example, when rabbits are kept as shown in Fig. 2, four rabbits are visible from any window and there are nine in total.

(1) There may be a room in which no rabbit is. 

Rabbits should be kept to be seen nine from any window. 

In this case, how many rabbits are there at least and how many rabbits at most?

(2) There is at least one rabbit kept in every room and 17 rabbits in total are kept in the hut. 

In order for 7 rabbits to be seen from any window, how many rabbits should be kept in each room? 

Answer one pattern in the figure.
For example, when putting in a rabbit as shown in Fig. 2, it should be answered as shown in Fig. 3. 

Math Problem : LL.15 Round-robin tournament in five teams

Five teams, A, B, C, D, and E held the round-robin tournament to which every team plays a game against other teams 1 time respectively.

The number of victories of A and B is same and that of C and D is same, too.

The sum total of the number of victories of these four teams is six.

Supposing A won B and C, answer the team which C won.

Suppose that there was no draw.

LL.14 Choose number from 1 to 10 by turns

Two persons choose a number from 1 to 10 by turns and sum up all numbers both choose.

They may also choose the same number many times.

When the sum total of the number of two persons becomes 100 or more, the person who chose the number at last is to be loser.

When the first person chose 8, which number should be chosen next in order for another person to certainly win?

LL.13 Guess the color of the card

There are one red card and two black cards. 

I pass these three cards to Taro, Jiro, and Hanako. 

They look at the color of their own and find the color of the card of other two. 

I asked Taro but Taro said "I can not find." 

Jiro heard the answer of Taro then said "I can guess by hearing the answer of Taro." 

What color is a color of three cards of three persons?

LL.12 Find a bag of fake gold coins

There are five bags in which a lot of gold coins are put and fake gold coins only are contained in one bag of them.

As for the weight of one piece of gold coin, the genuine one is 10 g and the fake is 8 g.

Is there any way to find the bag of fake gold coins by using only once the scales that can weigh pieces of gold together at a time ?

LL.11 Talk a rumor to ten persons

I heard others' rumor just now and I talked the rumor to ten persons ten minutes later. 

And these 11 persons talked it to ten persons respectively ten minutes afterward. 

Furthermore, all persons that heard this rumor talked to ten persons 10 minutes afterward, respectively. 

One hour after the time I heard the rumor first, how many persons know this rumor ? 

LL.10 Guess what I'm thinking

Father said to his son.

"Here is 1000 yen. If you can estimate what I consider, I will give you this 1000 yen." 

Is there any answer by which he can get 1000 yen ? 

LL.9 Guess the color of the hut being worn

There are three red hats and two white hats. 

After showing these hats to three persons, Taro, Jiro and Hanako, I put a hat on each person which can not be visible to each and hide remaining two hats. 

I asked the color of their own hat in order of Taro, Jiro and Hanako. 

Three persons should find the color of their own hat by looking at other hats of two persons. 

Taro and Jiro could not find but Hanako could find the color after hearing the answer of Taro and Jiro. 

What color is the color of the hat of three persons respectively ?

LL.8 Remain 5L in 7L vessel

There is a vessel of 3L, 4L, and 7L, and the scale is not attached on each. 

Water is in the vessel of 7L full. 

How many times as less as possible do you need leaving 5L in 7L vessel by using three vessels ?

LL.7 Take out 50kg gold dust

There are an even balance and one weight of 2 kg and 9 kg each. 

How many times as few as possible should I use even balance in order to take 50 kg gold dust out of a heap of gold dust in front of me ? 

I can use gold dust that was already weighed and taken as a weight.