Solution To – How Many Triangles Do You See?

How Many Triangles Do You See

How Many Triangles Do You See ?

Hello friends,

Here’s a fun challenge for you. How many triangles can you see (or count) in the diagram above?

If you intend to count them one by one, you will need some form of concentration – else you might lose count!

Here’s one of the method to count it :

How To Count The Triangles In The Diagram Systematically

First, lets label every corner with an Alphabet :

How Many Triangles Can You See - Solution A
 

Next, group the triangles from small to large triangles (or by sub triangles)

Example of a group of small triangle will be AFG, BCG, etc

Example of a group of triangles formed by 2 smaller triangles, ie. AGK, CGM

How Many Triangles Can You See - Single and Double Triangles




 
The ones that are commonly missed, are these Triangles formed by 9 smaller triangles, ie. APS and especially GVY

How Many Triangles Can You See - commonly missed formation

 

So, these are the Triangle Groups :

Single Triangles - Click The Drop Down Arrow To Reveal

Total Single Triangles = 32

  1. ABG
  2. AFG
  3. BCG
  4. CDI
  5. CGH
  6. CHI
  7. DEI
  8. EIJ
  9. FGK
  10. GHM
  11. GKL
  12. GLM
  13. HIM
  14. IJO
  15. IMN
  16. INO
  17. KLQ
  18. KPQ
  19. LMQ
  20. MNS
  21. MQR
  22. MRS
  23. NOS
  24. OST
  25. PQU
  26. QRW
  27. QUV
  28. QVW
  29. RSW
  30. STY
  31. SWX
  32. SXY

Double Triangles - Click The Drop Down Arrow To Reveal

Total Double Triangles = 24

  1. ACG
  2. AGK
  3. CEI
  4. CGI
  5. CGM
  6. CIM
  7. EIO
  8. GKM
  9. GKQ
  10. GMQ
  11. GIM
  12. IMO
  13. IMS
  14. IOS
  15. KMQ
  16. KQU
  17. MOS
  18. MQS
  19. MQW
  20. MSW
  21. OSY 
  22. QSW
  23. QUW
  24. SWY

Four Triangles - Click The Drop Down Arrow To Reveal

Total Four Triangles = 20

  1. ACK
  2. ACM
  3. AKM
  4. CEM
  5. CEO
  6. CKM
  7. CMO
  8. EMO
  9. GIQ
  10. GIS
  11. GQS
  12. IQS
  13. KMU
  14. KMW
  15. KUW
  16. MOW
  17. MOY
  18. MUW
  19. MWY
  20. OWY

 

Eight Triangles - Click The Drop Down Arrow To Reveal

Total Eight Triangles = 8

  1. AEM
  2. AMU
  3. CKO
  4. CKW
  5. COW
  6. EMY
  7. KOW
  8. MUY

Nine Triangles - Click The Drop Down Arrow To Reveal

Total Nine Triangles = 8

  1. ADS
  2. APS
  3. BEQ
  4. EQT
  5. FIU
  6. GJY
  7. GVY
  8. IUX

Sixteen Triangles - Click The Drop Down Arrow To Reveal

Total Sixteen Triangles = 4

  1. AEU
  2. AEY
  3. AUY
  4. EUY

THE ANSWER

So the Answer is :

32 + 24 + 20 + 8 + 8 + 4 = 96

There are 96 Triangles in the diagram.






 

How many of you got it right?

You are welcome to share this fun puzzle with your friends, and if you have some other challenging ones to mention, and would like to have it featured, let me know in the comment box below or you can write to me from my contact page.

 

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