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T he Main Challenge

Three UNIQUE digits from 1-9 must be used to arrive at today’s target number, 19, by multiplying two numbers together and either adding or subtracting the third number.

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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