# DAY/DYDD/PÄIVÄ/NAP 161 at 7puzzleblog.com T he Main Challenge

Three DIFFERENT digits from 1-9 must be used in a particular way to arrive at a specified target number. The rule is to multiply two numbers together, then either add or subtract the third number, so you arrive at today’s target number of 30.

As an example, one such way of making 30 is (8×3)+6. Can you find the other FOUR ways of making 30?

[Note:  (8×3)+6 = 30  and  (3×8)+6 = 30  counts as just ONE way] 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which THREE numbers, when 31 is added to each, all become square numbers? 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 161, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers The Target Challenge

Can you arrive at 161 by inserting 3810 and 15 into the gaps on each line?

•  ◯×◯++ = 161
•  (◯+◯)×(◯–◯) = 161   