# day/dydd 106 at 7puzzleblog.com T he Main Challenge

Here are seven more mental arithmetic questions for you to try:

1.  Which number multiplied by itself gives 196?
2.  What is 50 + 400 + 5?
3.  54 – 45 = ?
4.  If Jo runs 10 miles in one hour, how much further would she get in an extra 15 minutes running at the same rate?
5.  (14 – 3) × (7 + 2) = ?
6.  Which fraction comes next in the list: 1/12, 1/6, 1/4, 1/3, …
7.  How many days equal 6 weeks? 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

List FIVE different numbers that total 100. 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 SEVEN ways of making 106 when using Lagrange’s Theorem. Can you find them all? The Mathematically Possible Challenge

Using 14 and once each, with + – × ÷ available, which FIVE numbers is it 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 106 by inserting 4, 5, 6 and 7 into the gaps on both lines?

•  ◯²+◯²+◯²+◯ = 106
•  ³–(◯+◯)×double◯ = 106   