Level 2

Operations

    AA.1    Make formula using 3 four times       

    AA.2    Six digits integer        

    AA.3    Transformation of formula        

Properties

    BB.1

Ratios and proportions

    CC.1    Water and wine in two vessels        

    CC.2    Fold newspaper 20 times           

    CC.3    Number and cost price of apple     

    CC.4    Put in soy sauce by 1L       

    CC.5    Visitors' line at aquarium        

    CC.6    Cows in the pasture        

    CC.7    How old am I now?       

    CC.8    Admission ticket of a theater            

    CC.9    Water moves in three tanks            

    CC.10    Election of the president of student council        

    CC.11    Homework of summer vacation           

    CC.12    Discounted ticket price           

    CC.13    Bagging work by three persons            

    CC.14    Exchange salt solution between two        

    CC.15    Take out three kind of ball            

    CC.16    Set of apple and orange juice           

    CC.17    Donation by three persons           

    CC.18    Management of the party           

    CC.19    Test of three problems            

Problem solving (Velocity)

    DD.1    Passing every five minutes              

    DD.2    Go forth by three steps and back by two steps         

    DD.3    Whistle from express train         

    DD.4    Steam whistle from steam train              

    DD.5    Round trip of the mountain path            

    DD.6    Walk on 40 steps escalator           

    DD.7    Run around the pond           

    DD.8    Three persons start at different time           

    DD.9    Three persons run in the school ground            

    DD.10    Two way speed walking on the escalator       

    DD.11    Number of steps to catch up           

    DD.12    Time when passing each other             

    DD.13    Long-distance train           

    DD.14    Go to another town by bicycle and on foot        

    DD.15    Ten cars passing on the highway       

    DD.16    Two persons moving around a pond       

    DD.17    Two persons meet and janken           

    DD.18    Long hand and hour hand of flower clock        

    DD.19    Two persons' moving by bicycle       

    DD.20    Replacement of long and hour hand       

    DD.21    Change speed to catch up           

    DD.22    Two different styles of moving        

    DD.23    Bring balls to moving dray              

    DD.24    Speed ratio of two persons            

    DD.25    Pass traffic jam section            

    DD.26    Game walking around a pond            

    DD.27    Two persons go to house each other        

    DD.28    Time one passed another           

    DD.29    Notice an article left behind       

    DD.30    Town on the top of mountain          

    DD.31    Three persons from home to a park            

    DD.32    Moving by running and a car           

    DD.33    Two points between school and park        

    DD.34    Speed ratio is 7 : 5          

    DD.35    Triathlon race           

    DD.36    Library between school and station       

    DD.37    Another triathlon race            

    DD.38    Walk to the next bus stop           

    DD.39    Walking and running around a pond            

    DD.40    Load dropped to a river from ship        

    DD.41    Walk along riverside and ship in the river       

    DD.42    Change direction at every meeting            

    DD.43    Graph of distance of two persons           

    DD.44    Three points moving on three circles       

    DD.45    Carry an iron plate           

    DD.46    Four animals on a rectangle          

    DD.47    Carry water to cart            

Transformations

    EE.1    Two points moving on a diameter            

    EE.2    Water into three tanks           

    EE.3    One water feeding pipe and two draining pipes    

    EE.4    Partition in a water tank            

    EE.5    Telephone rate of two companies           

    EE.6    Travel distance and railway fare           

    EE.7    Length of a candle            

    EE.8    Special digital clock            

Problem solving (Sum and difference)

    FF.1    Fixed and proportional rate to send package           

    FF.2    Test of ten problems of O or X          

    FF.3    Test of four questions           

    FF.4    Three persons in the train       

    FF.5    Distribution of seeds of flower           

    FF.6    Gather flower petals in a schoolyard       

    FF.7    Pass money among three persons            

Number sense / theory

    GG.1    How many numbers of 0 in the product            

    GG.2    Number of times divided by 3           

    GG.3    Find two cakes among three         

    GG.4    Same departure time of two trains     

    GG.5    Share oranges with several persons                

    GG.6    Add 3 or 8 to a number        

    GG.7    Divide three numbers by the same number          

    GG.8    Sequence of integers after separation of each digit

    GG.9    Product of two integers is 44448888       

    GG.10    I was born in ABCD        

    GG.11    One integer added to 12 after another            

    GG.12    Operational rule of integers               

    GG.13    Sum of fractions whose numerator is 1       

    GG.14    Six light bulbs               

    GG.15    Repeat operation of integers            

    GG.16    Integers of remainder one divided by three       

    GG.17    Sum of two integers is divided by G.C.D.        

    GG.18    200---07 divisible by 27 and indivisible by 81        

    GG.19    Three digit integers divided by 35 and 40       

    GG.20    Paper tape is cut at 3, 5, 7 equal parts           

    GG.21    Year of Showa era and A.D.           

    GG.22    Integer divided by 4, 5, 7 with some remainder   

    GG.23    Three persons read books with different pages   

    GG.24    13 persons ordered one confectionery and drink  

    GG.25    Multiple of even numbers           

    GG.26    Quotient and remainder are same           

    GG.27    One number after another is multiplied from 1     

    GG.28    Sum of three integers is 1000            

    GG.29    1989 expressed by continuous integers        

    GG.30    Skip every 2 piece on the stones around a pond   

    GG.31    1/12 = 1/x + 1/y                           

    GG.32    Number of sheets of origami          

    GG.33    Price of consumption tax included            

    GG.34    Multiple of each number of digit            

Number of cases / Probability

    HH.1    Numbers with no 4           

    HH.2    Three pieces among red, blue, and black          

    HH.3    Share six oranges with four persons            

    HH.4    Another sharing six oranges         

    HH.5    Divide hexagon            

    HH.6    Connecting three points to be triangle           

    HH.7    Four wins and three losses at World Series           

    HH.8    Insect moving along the side of solid        

    HH.9    Election of three committees         

    HH.10    Two persons roll a die            

    HH.11    Arrange three numbers and alphabet       

    HH.12    Sum of each digit is 10            

    HH.13    Hexagon is divided by two diagonal lines        

    HH.14    Four figures containing 5          

    HH.15    Number of ways from P to A            

    HH.16    Tournament games of soccer in 7 teams       

    HH.17    Move of the side of regular tetrahedron      

Patterns / Regularity

    II.1    Number to buy to drink 100 bottles        

    II.2    Multiply 27 50 times          

    II.3    100th anniversary day of foundation             

    II.4    Number of days of Friday 13th         

    II.5    Make big equilateral triangle by putting small ones                

    II.6    No multiple of 9 and no 9 in any digit      

    II.7    Rearrangement of 12 cards          

    II.8    No number as a price including tax            

    II.9    Connect red tapes and white tapes          

    II.10    Arrangement of numbers and alphabets       

    II.11    Arrangement of numbers based on rules     

    II.12    Sequences on a certain condition          

    II.13    Sequences on a certain rule           

    II.14    Piled up two-face coins          

    II.15    Four numbers in square cards           

    II.16    Four empty bottles for one new bottle      

    II.17    (Deleted)       

    II.18    Number of teams are multiples of two in tournament

Geometry (Plane figure)

    JJ.1    Combination of two right triangles            

    JJ.2    Square in the right triangle       

    JJ.3    Rope going around the earth       

    JJ.4    Board on the roller            

    JJ.5    Coin rotating around another coin        

    JJ.6    Congruent two sectors           

    JJ.7    Area ratio of square and triangle        

    JJ.8    Extension of three sides of triangle       

    JJ.9    Division of square            

    JJ.10    Combining small equilateral triangles to be large one

    JJ.11    Disk rolls around another disk                

    JJ.12    Fold a rectangular paper                

    JJ.13    Area ratio of parallelogram           

    JJ.14    Area ratio of triangles           

    JJ.15    Triangle in hexagon           

    JJ.16    Combination of five equilateral triangles         

    JJ.17    Partition of square           

    JJ.18    Overlapped right angle triangles            

    JJ.19    Length in a triangle           

    JJ.20    Figure in two circles attached           

    JJ.21    Two squares and one circle           

    JJ.22    Straight lines with certain angles            

    JJ.23    Two persons move on a rectangle           

    JJ.24    Three angles in two figures            

    JJ.25    Folded and flattened paper tape       

    JJ.26    Rounded book            

    JJ.27    Partition of trapezoid            

    JJ.28    Overlapped two circles and rectangle        

    JJ.29    Ratio of area and length of sides           

    JJ.30    Partition of a circle           

    JJ.31    Four sectors in a square           

    JJ.32    Two circles with a shaded area        

    JJ.33    Trapezoid and three sectors            

    JJ.34    12 points on a circumference       

    JJ.35    Divide quarter sector into 36 portion        

    JJ.36    Bending paper tape right-angled         

    JJ.37    Fold and cut a rectangular paper          

    JJ.38    Fold a circle twice and open        

    JJ.39    Rotate triangle around a rectangle

    JJ.40    A circle moves around a figure        

    JJ.41    Rotation of a triangle

    JJ.42    Movement of rectangle overlapping triangle

    JJ.43    Four points on the side of rectangle

    JJ.44    Moving point on the side of rectangle

    JJ.45    Extension of sides of quadrangle

    JJ.46    Partition of rectangle and three points

    JJ.47    Partition of trapezoid to be triangle

    JJ.48    Partition of parallelogram to find area

    JJ.49    Six squares overlap sectors

    JJ.50    Overlapping of rectangle and circle

    JJ.51    Triangle and trapezoid

    JJ.52    Triangle in rectangle

    JJ.53    Partition of right hexagon

    JJ.54    Another partition of right hexagon

    JJ.55    Make right hexagon of parallelograms and trapezoids

    JJ.56    Divide rectangle into three figures

    JJ.57    Cut squares out of rectangular paper

Geometry (Solid figure)

    KK.1    Suitable lid for vessel

    KK.2    Development view of cube with numbers

    KK.3    Development view of quadrangular pyramid

    KK.4    Shadow of quadratic prism

    KK.5    Solid of revolution of trapezoid

    KK.6    Development view of cube

    KK.7    Cut cube to be development view

    KK.8    Triangular pyramid from rectangular paper

    KK.9    Solid with eight equilateral triangles

    KK.10    Assemble development view

    KK.11    Development view of rectangular prism 

    KK.12    Projection view of solid

    KK.13    Solid made by cutting quadrangular pyramid

    KK.14    (Deleted)   Pile up cubes on a square mat board

    KK.15    Accumulated cubes and paint

    KK.16    Shortest line on solid

    KK.17    Number of spots of dice

    KK.18    Sum of number of spots of dice

    KK.19    Difference of total surface area

    KK.20    Cut line on the development view

    KK.21    Another cut line on the development view

    KK.22    Put two rectangular prism into water

    KK.23    Three cylinders in water tank

    KK.24    Four solids in water tank

Logical reasoning

    LL.1    Numbers of stone taken out to make pair        

    LL.2    Find a fake gold coin          

    LL.3    "Janken" game among three persons       

    LL.4    Find the number of honest person        

    LL.5    Which house is whose          

    LL.6    Ranking of shogi game among three        

    LL.7    Take out 50kg gold dust        

    LL.8    Remain 5L in 7L vessel        

    LL.9    Guess the color of the hut wearing        

    LL.10    Guess what I'm thinking       

    LL.11    Talk a rumor to ten persons       

    LL.12    Find a bag of fake gold coins       

    LL.13    Guess the color of the card        

    LL.14    Choose number from 1 to 10 by turns      

    LL.15    Round-robin tournament in five teams

    LL.16    Rabbits in the hut

    LL.17    Seats of six persons

    LL.18    Tournament of soccer in eight teams

    LL.19    Find one heavy ball by even balance

    LL.20    (Deleted)  Four different volume of iron balls

    LL.21    Three persons take out red and white ball 

    LL.22    Play at dice using figure