# DAY 198: The Main Challenge

What is the LOWEST whole number that satisfies all three criteria below?

• it is the sum of five consecutive whole numbers,
• it is the sum of two consecutive odd numbers,
• it is the sum of three consecutive even numbers. The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

List five different numbers that have a sum of 70. 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 198 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable The Target Challenge

Can you arrive at 198 by inserting 467 and 9 into the gaps on each line?

•  (◯×◯–◯)×◯ = 198
•  (treble◯+◯×√◯)×◯ = 198 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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