day/dydd 248 at

T he Main Challenge

What is the lowest Prime Number total it is possible to achieve when adding together SEVEN unique non-Prime Numbers?

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 1st & 4th rows of the playing board contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the sum of the factors of 40?

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 just THREE different ways to make 248 when using Lagrange’s Theorem. Can you find them?

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?

2    4    6    8    10    12    14    16    18    20


The Target Challenge

Can you arrive at 248 by inserting 5, 7, 8, 10 and 12 into the gaps below?

  •  ◯³+√(◯+◯+◯)–◯² = 248

Answers can be found here.

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