# DAY/DYDD 237: T he Main Challenge

There are two sets of three consecutive numbers, in ascending order, whose sum is less than 50 and follow this sequence:

•   triangular number – square number – prime number

Can you list both sets of numbers? 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 3rd & 6th rows of the playing board contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

What is the difference between the totals of the odd numbers and even numbers? 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 ELEVEN different ways to make 237 when using Lagrange’s Theorem. How many of them can you find? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable The Target Challenge

Can you arrive at 237 by inserting 1, 2, 3, 4 and 5 into the gaps below?

•  (◯+◯)²×(◯+◯)–double◯ = 237 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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