2023 **Author**: Malcolm Clapton | [email protected]. Last modified: 2023-07-28 10:38

Guess what connections are between letters and numbers in the examples, and then fill in the cells with a question mark.

## – 1 –

Determine what number should be in the place of the question mark.

Instead of a question mark in a circle, there should be the number 253. This is the principle by which numbers in circles are formed: each previous one is multiplied by 2, and 3 is added to the result.

1 × 2 + 3 = 5.

5 × 2 + 3 = 13.

13 × 2 + 3 = 29.

29 × 2 + 3 = 61.

61 × 2 + 3 = 125.

125 × 2 + 3 = 253.

Or here's another solution: to each previous number, 2 is added to the n-th power.

1 + 2^{2} = 1 + 4 = 5.

5 + 2^{3} = 5 + 8 = 13.

13 + 2^{4} = 13 + 16 = 29.

29 + 2^{5} = 29 + 32 = 61.

61 + 2^{6} = 61 + 64 = 125.

125 + 2^{7} = 125 + 128 = 253.

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## – 2 –

Determine which letter should be in the place of the question mark.

Instead of a question mark, the letter "P" should be in the square. The sum of the numbers in each square is the ordinal number of a letter in the alphabet. Let's check:

6 + 4 + 4 = 14. "M" is the fourteenth letter in the alphabet. We also count "Yo"!

4 + 1 + 7 = 12. "K" is the twelfth letter in the alphabet.

5 + 6 + 10 = 21. "U" is the twenty-first letter in the alphabet.

1 + 14 + 2 = 17. "P" is the seventeenth letter in the alphabet, which should be in place of the question mark.

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## – 3 –

Determine what number should be in the place of the question mark.

Instead of a question mark, there should be the number 179. If you move clockwise starting from 3, then each subsequent number is equal to twice the previous one, to which 1, 3, 5, 7, 9 have been added.

3 × 2 + 1 = 7.

7 × 2 + 3 = 17.

17 × 2 + 5 = 39.

39 × 2 + 7 = 85.

85 × 2 + 9 = 179.

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## – 4 –

Determine what number should be in the place of the question mark.

Instead of a question mark, there should be number 11. To get each number from the left half of the circle, we take a number from the opposite sector, double and add one.

5 = 2 × 2 + 1.

7 = 3 × 2 + 1.

9 = 4 × 2 + 1.

11 = 5 × 2 + 1.

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## – 5 –

Determine what number should be in the place of the question mark.

Instead of a question mark there should be the number 66. If you move clockwise starting from 4, each subsequent number is equal to twice the previous one, from which two was subtracted.

4 × 2 − 2 = 8 − 2 = 6.

6 × 2 − 2 = 12 − 2 = 10.

10 × 2 − 2 = 20 − 2 = 18.

18 × 2 − 2 = 36 − 2 = 34.

34 × 2 − 2 = 68 − 2 = 66.

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