# DAY 175: The Main Challenge

Three people answered four multiple choice problems each, with a choice of A B or C, and their responses are shown here:

• Tim:    A  B  B  C
• Tam:   A  C  B  A
• Tom:   B  B  C  A

If two people answered two questions correctly and one person had them all wrong, can you work out what the correct answers could be? 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Which of the square numbers listed has the most number of factors? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 175, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1    3    5    7    9    11    13    15    17    19

#OddNumbers The Target Challenge

Can you arrive at 175 by inserting 1, 5, 10 and 15 into the gaps on each line?

•  ◯²+(◯×◯×◯) = 175
•  ◯²–(◯×◯×◯) = 175
•  (◯+◯)×◯+double◯ = 175
•  (◯+◯)×◯+treble◯ = 175 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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