# day/dydd 15 at 7puzzleblog.com The Main Challenge

Your task is to multiply two numbers together and then subtract a third number to achieve the target answer of 7. The three numbers used in each calculation must all be unique digits from 1-9.

For example, one such way of making 7 is (4×3)5. Can you find SIX other ways to make 7?

[Note:  (4×3)5 = 7  and  (3×4)5 = 7  counts as ONE way.] The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the difference between the total of the prime numbers and the sum of the multiples of 10? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There is only ONE way of making 15 when using Lagrange’s Theorem. Can you find it? The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 15 by inserting 2, 3, 5 and 6 into the gaps on each line?

•  ◯×◯+◯◯ = 15
•  ◯÷×²×◯ = 15
•  ◯²–(◯+◯)× = 15   