# day/dydd 61 at 7puzzleblog.com

T he Main Challenge

Read the information below to find each of these three different numbers:

•  A is the only 2-digit square number that does not contain any odd digits
•  B is the only 2-digit prime number with both its digits the same
•  C is the only 2-digit cube number less than 50

Calculate the sum of AB and C.

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 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the sum of the even numbers listed?

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 FOUR ways of making 61 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which is the ONLY number it is 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 61 by inserting 3, 5, 8 and 10 into the gaps on each line?

•  ◯×◯++ = 61
•  (◯–◯)×◯+ = 61
•  (◯+◯)×◯+double = 61
•  (◯+◯)×◯–half = 61

Answers can be found here.

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