Subjects number patterns

Cell Numbers Completion

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Cell Numbers Completion


1. The problem presents hexagonal shapes with numbers on the left edge, inside, and the right tip, with the goal to complete the sequences based on an example. 2. From the top-left graph example: left edge is 3,4,9,5,6; inside is 13; right tip is 99. 3. Observing the pattern, let's analyze how 99 relates to the others. It seems the numbers inside and on edges combine or transform to produce the tip. 4. Checking sums of left edge numbers: $3 + 4 + 9 + 5 + 6 = 27$. Inside is 13. Sum of 27 and 13 is 40, which doesn't equal 99. 5. Trying another method: consider the product of inside and sum of left edge: $13 \times 27 = 351$, not 99. 6. Trying sum of inner number and specific pairs: for example, $13 + 9 + 5 = 27$, still no. 7. Next, let's check if the right tip equals sum of left edge squared minus the inside number: $27^2 - 13 = 729 - 13 = 716$, no. 8. Given this, let's examine the other examples to find a general pattern. 9. Top-right graph: left edge 9,8,2,7; inside 20; right tip 47. 10. Sum of left edge: $9 + 8 + 2 + 7 = 26$, inside 20; sum 46 roughly near 47. 11. Plus 1 difference, maybe right tip is sum of left edge plus the inside plus 1: $26 + 20 + 1 = 47$, matches. 12. Check bottom-left graph: left edge 8,8,2,7,8 sum is $8 + 8 + 2 + 7 + 8 = 33$, inside 43, total $33 + 43 = 76$, right tip is 88 which is 12 more. 13. Try difference: $88 - 43 = 45$, $45 - 33 = 12$, no clear simple relation. 14. Now let's try bottom-right: left edge 8,7; inside numbers 5,6; right tip 50. 15. Sum left edge: $8 + 7 = 15$, inside sequence sum $5 + 5 + 6 = 16$, total $15 + 16 = 31$, right tip is 50. 16. Difference $50 - 31 = 19$ no clear simple addition. 17. Given ambiguity, the instructions in Arabic say: "Complete numbers in the cells as in the example." The example with hex for first figure shows left edge and inside leading to a right tip. 18. A reasonable educated guess: the right tip number is sum of all numbers inside and on the left edge. 19. Then, for each missing number, solve to make the sum consistent with the observed right tip. 20. For top-right graph: Left edge: 9,8,2,7 = 26 Inside: 20 Right tip: 47 Calculate sum: 26 + 20 = 46, need 47 right tip, so possibly right tip = sum + 1. 21. Therefore, complete numbers to maintain sum + 1 rule, for bottom-left and bottom-right do similar. 22. Final answers for missing cells (assuming pattern sum of left edge + inside + 1 equals right tip): Top-right: given correct. Bottom-left: left edge sum 33 + inside 43 = 76, right tip 88, difference 12, so we assign missing numbers to fit sum + 12 rule. Bottom-right: left edge sum 15; inside total of 5,6 plus missing 5 to be checked. This problem requires more data or clearer instructions for exact values for each missing cell, but the above reasoning summarizes the approach. Final result: missing numbers should be assigned such that sum(left edge numbers) + inside numbers (+ possibly a constant) equals the right tip number.