DAY/DYDD 63:

The Main Challenge

Which is the only digit not represented when listing the square numbers from 10² to 19²?

The 7puzzle Challenge

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

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Find three different numbers that have a sum of 100.

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 FOUR ways of making 63 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

The Target Challenge

Can you arrive at 63 by inserting 3, 3, 4 and 5 into the gaps on each line?

  •  ◯×◯×◯+ = 63
  •  ◯²×◯–× = 63
  •  ◯×◯×(◯+√◯) = 63

Answers can be found here.

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