In the 4×4 grid shown, each of the four symbols has a different value. The sum of the values of the symbols in each row is given to the right of that row.Hide/Reveal Grid Description Row 1 has a heart, triangle, triangle, heart. The number on the right is 26. Row 2 has four triangles. The number on the right is 24. Row 3 has a square, diamond, heart, diamond. The number on the right is 27. Row 4 has a square, heart, square, triangle. The number on the right is 33. What is the value of ⧫?
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Solution
From the second row, △+△+△+△=24 or 4△=24, and so △=6. From the first row, ♡+△+△+♡=26 or 2♡+2△=26. Since △=6, then 2♡=26−12=14, and so ♡=7. From the fourth row, □+♡+□+△=33. Since △=6 and ♡=7, then 2□+7+6=33, and so 2□=20 or □=10. Finally, from the third row, □+⧫+♡+⧫=27. Since □=10 and ♡=7, then 2⧫=27−10−7=10. Thus, ⧫=5.
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