# DAY 157:

The Main Challenge

Using each of the decimal numbers 0.1, 0.2, 0.3 and 0.4 once only, and with the four arithmetical operations + – × and ÷ available, show how you can arrive at the target answer of 7.

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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the sum of the 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 157, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using the three digits 35 and 8 once each, with + – × ÷ available, which are the only TWO numbers it’s possible to make from the list below?

8    16    24    32    40    48    56    64    72    80

#8TimesTable

The Target Challenge

Can you arrive at 157 by inserting 7810 and 11 into the gaps below?

•  ◯×◯+◯×◯ = 157