Logic puzzles: 12 number and figure series
Puzzle 1 · number series
2 · 6 · 18 · 54 · 162 · ?
Which number replaces the question mark?
Show the answer and the rule
C 486. Each number is three times the one before, so 162 × 3 = 486. You get 270 by adding the last difference of 108 again. 386 is a slip in the multiplication where the carried hundred gets lost. 1458 belongs one place further on.
Puzzle 2 · figure series
Four figures. In order, figure 1 shows a black circle; figure 2 shows a black square; figure 3 shows a black triangle; figure 4 shows a black circle. Then a question mark.
Which figure comes next?
Show the answer and the rule
A Black square. The shape goes round in a fixed order of circle, square and triangle, then starts again. After the second circle comes a square, and everything stays black. The triangle skips the square, and the circle repeats the last figure. The white square has the right shape with a colour that never appears in the row.
Puzzle 3 · number series
3 · 5 · 8 · 12 · 17 · ?
Which number replaces the question mark?
Show the answer and the rule
A 23. The differences are 2, 3, 4 and 5, so the next step adds 6 and you get 23. You land on 24 if you let the step grow by 2. 27 doubles the last difference of 5. 30 is two steps ahead, 17 + 6 + 7.
Puzzle 4 · figure series
Four figures. In order, figure 1 shows a arrow pointing down, two dots; figure 2 shows a arrow pointing left, two dots; figure 3 shows a arrow pointing up, two dots; figure 4 shows a arrow pointing right, two dots. Then a question mark.
Which figure comes next?
Show the answer and the rule
C Arrow pointing down, two dots. Down, left, up, right: the arrow turns a quarter clockwise each time, so it points down again. The two dots stay the same. Left is one quarter turn too many. Up is what you get when you turn anticlockwise. The arrow pointing right is figure 4 once more.
Puzzle 5 · figure series
Four figures, each a 3 by 3 grid with a shape in the middle cell. In order, figure 1 shows a black cell at the top left, black square; figure 2 shows a black cell at the top middle, black square; figure 3 shows a black cell at the top right, black square; figure 4 shows a black cell at the middle right, black square. Then a question mark.
Which figure comes next?
Show the answer and the rule
A Black cell at the bottom right, black square. The black cell moves one place clockwise around the edge of the grid each step, so after the middle right it goes down to the bottom right. The square stays black. Bottom left comes from reading the grid like a page and jumping to the start of the bottom row. Top right goes back, anticlockwise, and bottom middle is two places ahead.
Puzzle 6 · number series
1 · 5 · 13 · 29 · 61 · ?
Which number replaces the question mark?
Show the answer and the rule
D 125. The rule is times 2 plus 3, so 61 × 2 + 3 = 125. 122 only doubles and forgets the plus 3. 64 skips the doubling and only adds 3. 93 is 61 plus the last difference of 32.
Puzzle 7 · figure series
Four figures. In order, figure 1 shows a arrow pointing down, one dot; figure 2 shows a arrow pointing left, two dots; figure 3 shows a arrow pointing up, three dots; figure 4 shows a arrow pointing right, four dots. Then a question mark.
Which figure comes next?
Show the answer and the rule
A Arrow pointing down, five dots. The arrow turns a quarter clockwise each step, from down through left, up and right back to down. One dot is added every time, so four becomes five. Up with five dots turns back anticlockwise. Down with four dots forgets the extra dot. Up with four dots makes both mistakes.
Puzzle 8 · number series
0 · 3 · 8 · 15 · 24 · ?
Which number replaces the question mark?
Show the answer and the rule
B 35. Each number is a square minus 1, from 1 × 1 up to 5 × 5, so next comes 6 × 6 - 1 = 35. 36 forgets the minus 1. 33 is 24 plus the last difference of 9. 48 is 7 × 7 - 1, one place too far.
Puzzle 9 · figure series
Four figures. In order, figure 1 shows a white triangle, no dots; figure 2 shows a white circle, one dot; figure 3 shows a white triangle, two dots; figure 4 shows a white circle, three dots. Then a question mark.
Which figure comes next?
Show the answer and the rule
B White triangle, four dots. Triangle and circle take turns, so after the circle comes a triangle. The number of dots goes up by one each step, from none to three, and now four. The circle with four dots keeps the old shape. The triangle with three dots forgets the extra dot. The circle with three dots is figure 4 once more.
Puzzle 10 · number series
4 · 9 · 7 · 12 · 10 · 15 · ?
Which number replaces the question mark?
Show the answer and the rule
A 13. The row takes turns adding 5 and taking away 2, and 10 to 15 was plus 5, so now 15 - 2 = 13. Read as two series (4, 7, 10 and 9, 12, 15), both rise by 3 and you reach the same answer. 20 adds 5 once more, and 17 adds 2 where it should take 2 away. 18 continues the wrong series, 9, 12, 15.
Puzzle 11 · figure series
Four figures, each a 3 by 3 grid with a shape in the middle cell. In order, figure 1 shows a black cell at the bottom left, arrow pointing right; figure 2 shows a black cell at the bottom middle, arrow pointing down; figure 3 shows a black cell at the bottom right, arrow pointing left; figure 4 shows a black cell at the middle right, arrow pointing up. Then a question mark.
Which figure comes next?
Show the answer and the rule
D Black cell at the top right, arrow pointing right. The cell and the arrow each go their own way. The cell moves anticlockwise around the edge, from the middle right up to the top right. The arrow does turn clockwise, a quarter per step, and after up it points right. Bottom right moves the cell clockwise. Top right with the arrow pointing left also turns the arrow the wrong way. Top middle with the arrow pointing left does that and moves the cell two places.
Puzzle 12 · number series
3 · 5 · 11 · 29 · 83 · ?
Which number replaces the question mark?
Show the answer and the rule
A 245. Each number is the one before times 3 minus 4, so 83 × 3 - 4 = 245, and the differences 2, 6, 18 and 54 grow by times 3 as well. 249 forgets the minus 4, and 253 adds 4 instead. 731 is the number after that.
Pick an answer and your score starts counting. 12 puzzles to go.
Twelve logic puzzles with a number series or a figure series in each. Find the rule, pick the next number or figure, and see straight away whether you were right and why. The score at the bottom counts how many you get right.
The three kinds of series
Most logic puzzles in a series come in three kinds. In a number series you find the next number in a row such as 3, 5, 8, 12, 17. In a figure series a drawing changes from one box to the next, and you pick the drawing that comes after the last one. A letter series works like a number series with the alphabet: you count places, so A, C, E skips one letter each time. This page has six number series and six figure series. We left letter series out, because a letter rule often depends on the language you count in.
How to spot the rule in a number series
Write the differences between the numbers underneath the row. If they are all the same, you have a fixed step. If the differences grow or shrink, look at the differences of the differences: 2, 3, 4, 5 grows by one, so the next step is 6. When the numbers grow fast, try dividing instead: in 2, 6, 18, 54 each number is three times the one before. Some rows use two operations in one step, such as times 2 plus 3. Others take turns, adding 5 and then taking away 2, or weave two rows into one, where every other number belongs together. Squares are the last rule worth knowing by heart: 1, 4, 9, 16, 25, sometimes with a number added or taken away.
How to spot the rule in a figure series
In these figures, five things can change: a black cell that moves around the edge of a 3 by 3 grid, an arrow or triangle that turns, a fill that switches between black and white, a number of dots that goes up or down, and a shape that goes round in a fixed order. Never more than two of them change in one puzzle. Look at one feature at a time and follow it through every figure. First the position of the cell, then the direction, then the dots. Once you know the rule for each feature, build the next figure in your head and only then look at the four answers. Whoever looks at the answers first tends to pick the one that resembles the rest most, and the wrong answers here are built from real mistakes: turning the wrong way, moving one place too far, or forgetting the second feature.
Why assessments use series
Series need no knowledge of a subject or a language. Everything you need is in the row itself, so two people with very different schooling start from the same place. That is why number series and figure series turn up in so many aptitude tests and logic tests for jobs and training courses. In those tests you usually get a few minutes for a block of questions, and an open question counts as wrong. If a rule does not come within a minute, the usual advice is to move on and come back later.
What Skillido keeps
Nothing. Your answers and your score stay in this page and are gone when you close it. We do not ask for an account and we do not send your answers anywhere.
More to play
For twenty more questions with number series and conclusions from statements, try the logical reasoning test. The Thinking Check has five short games against the clock, and all other games are on the thinking games page. If you read Dutch, the same kind of puzzles are explained on logische puzzels.
Frequently asked questions
- How do these logic puzzles work?
- Each puzzle is a row of numbers or figures that follows one rule, sometimes two. You pick the answer that continues the row. Straight after your pick you see whether it was right, and the explanation opens with the rule and the mistake behind each wrong answer.
- What is a good score?
- We do not give a pass mark or compare you with other people, because too few people have solved this set to say anything about averages. Your score is how many of the twelve you got right, which you can compare with your own score next time.
- Is this a number sequence test like the ones employers use?
- The format is the same: a row of numbers or figures and four answers. Aptitude tests for jobs often have a clock and more questions in a row. This page has no clock, so you can take the time to find the rule and read why the other answers are wrong.
- Is my score saved?
- No. Your answers stay on this page and are gone when you close it or press Start again. There is no account and we do not count your answers.