DAY/DYDD 130:

The Main Challenge

Can you place the 12 numbers 1 1 2 2 3 3 4 4 5 6 7 and 8 into the 12 gaps below so that all four equations work out arithmetically?

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

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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 difference between the sum of the multiples of 8 and the sum of the multiples of 7?

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 TEN ways of making 130 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 130 by inserting 2, 3, 5 and 10 into the gaps on each line?

  •  (◯+◯)×◯×◯ = 130
  •  (◯×◯–◯)×◯ = 130
  •  ◯²+◯²+◯²–◯² = 130

Answers can be found here.

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