T he Main Challenge

Three UNIQUE digits from 1-9 must be used to arrive at a specified target number by multiplying two numbers together and either adding or subtracting the third number.

Today, your goal is to make 19.  The three numbers in each calculation must be different.

One way to make 19 is (7×2)+5, can you find the other THIRTEEN ways?

[Note:  (7×2)+5 = 19 and  (2×7)+5 = 19 counts as just 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 3rd & 6th rows of the playing board contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the sum of the multiples of 5 listed above?

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 are SIX different ways to make 239 when using Lagrange’s Theorem. How many of them can you find?

The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

6    12    18    24    30    36    42    48    54    60


The Target Challenge

Can you arrive at 239 by inserting 1235 and 6 into the gaps below?

  •  (◯+◯)²×◯–◯×◯ = 239

Answers can be found here.

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