DAY/DYDD 110:

T he Main Challenge

Carry out these instructions in our 7-step challenge:

  1.  Work out the sum of 4 and 6,
  2.  Calculate the product of 4 and 6,
  3.  Find the difference between the two answers in Points 1 and 2,
  4.  Square the answer to Point 3,
  5.  Subtract 75 from your answer in Point 4,
  6.  Find the square root of your answer in Point 5,
  7.  Multiply your answer in Point 6 by 10.

What is your final answer?

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 & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the product of the smallest and largest numbers on this list?

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 ways of making 110 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 110 by inserting 6, 7, 8 and 10 into the gaps on both lines?

  •  (◯+◯)×◯+◯ = 110
  •  (◯+◯)×◯+double◯ = 110

Answers can be found here.

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