DAY/DYDD 25:

The Main Challenge

One simple rule – multiply two numbers together, then either add or subtract the third number to achieve your target number of 10.  The three numbers used in each calculation must be unique digits from 2-9.

As an example, one such way of arriving at 10 is by (4×3)–2.  Can you find the FIVE other ways of making 10 using this rule?

[Note:  (4×3)–2 = 10  and  (3×4)–2 = 10  would count 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 2nd & 4th rows contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

What is the sum of the multiples of 8?

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 THREE ways of making 25 when using Lagrange’s Theorem. Can you find them?

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?

50    51    52    53    54    55    56    57    58    59

#NumbersIn50s

The Target Challenge

Can you arrive at 25 by inserting 2, 5, 10 and 20 into the gaps on each line?

  •  ◯²×◯×◯÷◯ = 25
  •  ◯+◯+◯÷◯ = 25
  •  ◯÷◯×(◯–◯) = 25

Answers can be found here.

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