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Math problems and brain teasers

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Number puzzles as math training and mental jogging

The puzzle system used at Mathematical-Puzzles.com is available in two versions which can either be solved online or in part downloaded as a PDF file. Altogether 378,028 math puzzles are available free of charge.

The simplified version is aimed mainly at pupils from Class 2 of the primary/ elementary school (7 years +), who can use it to practice the four basic arithmetical skills. The feeling of success will generate enthusiasm for math. In the math problems five numbers between 1 and 9 are combined using multiplication, division, addition and subtraction. How many numbers are provided in advance as 'clues' depends on the level of difficulty selected. Select math problems with 5 numbers and solve them online.

Because of its demands in terms of mental arithmetic, concentration, logic and memory the full version of the number puzzles appeals in particular to young people and adults who wish to increase and retain their mental fitness and enjoy solving problems. Nine numbers are combined by means of the four basic arithmetical skills - and the rule about multiplication/division ahead of addition/subtraction doesn't apply! Select math problems with 9 numbers and solve them online.

Rules:

You enter a number from 1 to 9 in the squares in such a way that they match the solution. Numbers can only be used once.
(In the full version the rule about multiplication/division ahead of addition/subtraction doesn't apply)

Example for pupils (medium):

2, 4 and 8 have already been used – this leaves us with 1, 3, 5, 6, 7 and 9 for the empty squares. First we need a number which, when it's multiplied by four, can be divided by 8. This is only possible with 6, which means that we divide 24 by 8 and are left with 3. What do we need to add to 3 so that when we take away 2 the result is 4? Correct, the answer is 3. The solution is therefore:
4 x 6 ÷ 8 + 3 - 2 = 4

Example of the full version (medium):

In this example 2, 5, 6 and 9 remain available for the empty squares. With this puzzle we start at the end: 8 x 8 is 64, which means that we need a number which, when added to 64, can be divided by 3. The only possibilities here are 2 and 5 (giving 66 or 69). With a few "what if" calculations we soon find that the 2 can't be right, which means that working backwards we have an intermediate result of 23 to the 3 in the seventh field. Now fields 4 and 6 are decisive, because afterwards it has to be possible to divide the intermediate result by 7, which provides a good opportunity to exclude incorrect combinations. After some trial and error we can clearly place the 2 in the fourth square and the 6 in the sixth square (leaving only the 9 for the second square). The solution is therefore: 1 + 9 x 7 - 2 ÷ 4 + 6 x 3 - 5 ÷ 8 = 8
(without applying the multiplication/division ahead of addition/subtraction rule!)

There are 50,456 math problems for children and 327,572 brain teasers for young people from 10 years upwards – divided into a range of different patterns and levels of difficulty. All the problems have only a single solution and are limited to whole numbers without decimal points.