# DAY/DYDD/GIORNO/NAP 152: Th e Main Challenge

Using the three numbers 1, 2 and 4 just once each, with + – × ÷ available to you, what is the lowest positive number it is NOT possible to make? 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 & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

Which TWO numbers listed have exactly four factors each? 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 (4+1+1+1).

Show how you can make 152, in THREE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 26 and 9 once each, with + – × ÷ available, which are the only FOUR numbers it’s possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

#PrimeNumbers The Target Challenge

Can you arrive at 152 by inserting 4810 and 12 into the gaps on each line?

•  ◯×◯+◯×◯ = 152
•  (◯+◯)×◯–◯ = 152 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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