# DAY/DYDD 54: The Main Challenge

Solve this Octaplus puzzle by finding the values of the eight letters, A to H, from the given clues. Each letter contains a different whole number in the range 1-32:

1.  D minus B is an even number,
2.  a third of D is an even number,
3.  G minus B is either 16 or 17,
4.  C is half of G, and E is half of C
5.  H is a third of B,
6.  D is equal to C plus H,
7.  F is either 18 or 20,
8.  A is 120 minus the sum of the other seven numbers. 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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which three different numbers from the list have a sum of 77? 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 FIVE ways of making 54 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

80    81    82    83    84    85    86    87    88    89

#NumbersIn80s

The Target Challenge

Can you arrive at 54 by inserting 2, 5, 8 and 12 into the gaps on each line?

•  ◯×◯+◯+◯ = 54
•  ◯×◯+◯–◯ = 54
•  (◯–◯)×◯–◯ = 54
•  (³√◯+◯÷◯)×◯ = 54 Answers can be found here. Click Paul Godding for details of online maths tuition. This entry was posted in 7puzzleblog.com. Bookmark the permalink.

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