Sudoku tutorial #86 Only 17 numbers to start!

[@isaiasprestes]

I really do love this channel!

[@SudokuGuy]

Gee thanks Isaias. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@twinkletime2982]

@@SudokuGuy I’m right with him. The best Sudoku channel on YT!

[@havishayadala9773]

Sudoku was damn difficult for me and i always gave up in the middle . and I started watching your videos recently and i can finally solve a sudoku puzzle successfully. Thank you so much!!!

[@SudokuGuy]

Thank you Havisha for your support. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@blueswallowtail4628]

Me too! I could only do the easy & moderate puzzles. Now, I'm up to expert puzzles. Whoo hooo!

[@SudokuGuy]

Congratulations Blue

[@blueswallowtail4628]

I'm 59 yrs old, had all my Teachers were as clear & concise as you, I'm sure I would have been a genius, lol. You're the greatest!

[@SudokuGuy]

Wow, thanks! Blue Please tell others about Sudoku Guy

[@leonarddickerson583]

Your methodically working through the puzzle was helpful and made it look simple. Thanks for the presentation.

[@SudokuGuy]

Glad it was helpful Len. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@howardpink8600]

Wonderful puzzle with lesson learning techniques. Thanks Robin.

[@SudokuGuy]

My pleasure Howard. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@NOCKSCITNEY]

I had to restart this puzzle numerous times (because I made mistakes) however for me, finding a 6 unlocked the whole puzzle for me. I've been trying to improve my game now for weeks and I think my biggest sticking points on puzzles is the reluctance to enter pencil marks when there are more than 2 place the number can go in the block. Having gone through some of the tutorials on this channel, I've learnt it's fine to put more than 2 of the same number in the block and in turn, it's helped me to not get stuck so much. Thanks for all your videos and tutorials, they really help in a simple, easy to follow format :)

[@SmartHobbies]

Thanks for sharing this. I think you are really starting to understand how to solve the more difficult puzzles. I’m glad you were able to solve this puzzle.

[@SudokuGuy]

Thanks for your comment. always something to learn with sudoku. Happy watching and learning. NOCK. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@panagiotissousamlis9025]

You make it to be so easy like magic , you are a great teacher thank you.

[@SudokuGuy]

You're very welcome! So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@burton2b]

Great Job Robin . . . you make it look easy!

[@SudokuGuy]

Thanks 👍 Buddy. Let's chat soon. We are very busy now getting ready to move hoefully for the last time.

[@rosesmith1111]

You are amazing at this! We appreciate you so much. Keep it up.

[@SudokuGuy]

You're the best! Hannah. Thanks for your support. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@ermelitaocampo1269]

Thanks i got it

[@kaylemoine1571]

Good puzzle. Easy to follow solving. Thank you.

[@SudokuGuy]

You are welcome! So glad you found my site Kay .“the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@licaleu5784]

Thank you so much for you videos. Just found your channel today and I enjoy your friendly and calm way of explaining ☺️👍 I will watch a lot more of your videos in the future 😊

[@SudokuGuy]

Glad you like them! So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@ryanmartin139]

Love your videos!

[@SudokuGuy]

Glad you like them! So glad you found my site."the most popular site online to learn sudoku" Please share with others, subscribe and click the bell by the subscribe button. Have fun as you learn step by step how to solve. For a list of videos go here: kzbin.info/door/d8JaOdfEWcJOtwG6YayW0w sudokuguy.com

[@birchandghoshdastidar1322]

Thank God! I could solve it in one attempt taking a reasonable time. Trained by sudoku Guy, Lucky me, may others also try!

[@SudokuGuy]

You can do it! Well done. It goes to show that a small set of numbers in a puzzle can be solved. Well done. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@rudiauer1444]

Thank you. Great teacher.

[@SudokuGuy]

You are welcome! Rudi. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@ayanbanerji2886]

Which software please tell

[@SudokuGuy]

Look underneath the video in the description and it will tell you. "enjoy sudoku" app

[@aharrypotterhead3025]

I really enjoy watching your videos :D I love sudoku and found my love to sudoku when I was a little child and I can say I'm quite good and quick at it, but still there are More techniques to learn, and you really helped a lot 😄

[@SudokuGuy]

That is awesome! So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@miaash3870]

Merry Christmas to you and your Mrs.

[@SudokuGuy]

Happy holidays! yo you and your partner too.

[@SmartHobbies]

Nice puzzle to showcase. I like how you explain how to find the pointing pairs of 6’s and 8’s. I also like the user interface. Will we ever see the whiteboard again?

[@SudokuGuy]

Glad it was helpful!Yes you will see it it soon as i just found out it will arrive before Xmas. Whoooppppeeee! Robin

[@dogyaltshering9653]

Wow That was fun. Thank you Sudoku Guy....I have become a Ninja owing to you

[@SudokuGuy]

Hello Doygal. thanks for your support. Please tell others

[@NimeshSadadiwala]

Can't believe we started with 17 numbers and with all easy ways we solved it. Thanks for your teaching and waiting for that whiteboard and colorful markers

[@SudokuGuy]

Keep it up Nimesh and thanks for your support. I hope to get the white board before the New Year. Compliments of the season. Robin

[@joebarajas4935]

Robin: Congrats on making it “down under” Stay safe best wishes And Saludos from South Texas

[@SudokuGuy]

HI Joe. compliments of the season. I'm still waiting for my shipment from Canada. Hope it arrives soon.

[@kennethhorne104]

Thank you my friend. You have taught me so much. I love soduko.

[@SudokuGuy]

Happy to hear that! So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@migoshungo3324]

Thank you my friend for sharing your tutorial video, I enjoy watching...

[@SudokuGuy]

Thank you! Cheers! Migo.

[@cmcn1]

Those tricks with the upside down T and right-side up T really are great. Some tricks I was using and did not even know it so I have added to my tool kit. Thank you very much for the tutorial.

[@SudokuGuy]

Happy to help! you addd a few more tricks to your list of techniques. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@byronrobbins8834]

@@SudokuGuy you shall be happy when your whiteboard arrives.

[@SoRTs6233]

Hi Robin, your sweetheart Catherine is absolutely right, it is possible to do without pencil marks. But I still watched your solution to see how you went through the steps. My sweetheart, Sheena, introduced me to Sudoku, and could always do difficult ones. But, through your tutorials that I eventually became better and now I do the one's she gives up on. Thanks for your help. Happy New Year to you both and, here's hoping, life will be good for you in Australia. Cheers, Jim L

[@SudokuGuy]

Wonderful! Jim/ Happy New Year.

[@rokibalboa840]

Good job, sir.

[@SudokuGuy]

Thank you kindly Ricki. thanks also for your support. Please tell others

[@ateeqah12398]

Superb...!

[@SudokuGuy]

Thanks a lot Ateeq So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@theboss20122015]

Where can I find the Soduko electronic version you are using. Thanks

[@SudokuGuy]

Hello Andrew ....go to the app store and enter sudoku. Scroll down until you come to "enjoy sudoku" by jason linhart. Pick the Heart version and you will be rewarded I use this app a lot I used this app when my famous white board was stuck on the pacific ocean as it was being transported from Canada to Australia. Robin

[@theboss20122015]

@@SudokuGuy Thank you so much for your quick response. Hope you get your white board very soon.

[@luishectormejiaflores]

... r5c9=(5,9)=3 (4,2)=3 (5,3)=6 (3,2)=6 Matching pair= par (3,8) en 6a col dentro del bloque 8; (6,2)=8; cuaterna=quad (1,2,4,5) dentro del bloque 4 ent único lugar (4,1)=1; haciendo TMB (6,6)=1 (6,3)=5 quedando el par (2,4) en 1a col dentro del bloque 4; haciendo LCR (9,3)=2 (8,3)=3 (8,6)=8 (9,6)=3 (7,9)=2 (3,8)=2 (1,6)=2 (5,5)=2 (5,1)=4 (6,1)=2; tercia (1,4,9) en 3a col dentro del bloque 1 ent (1,2)=5 (2,1)=7 (3,1)=8; haciendo LCR (9,1)=9 quedando la tercia (1,4,7) en 2a col dentro del bloque 7; haciendo TMB (6,4)=4 (5,4)=7 (4,4)=8 (5,8)=8 quedando la tercia (6,7,9) en 6a fila dentro del bloque 6 ent (4,8)=5 (5,6)=5 quedando el par (6,9) en 4a fila dentro del bloque 5; cuaterna (3,5,6,9) en 4a col ent único lugar (1,4)=9 (7,4)=5 (3,4)=3 (2,4)=6 (2,6)=4 quedando el par (1,5) en 5a col dentro del bloque 2; par (6,9) en 6a col ent (7,6)=9 (4,6)=6 (4,5)=9 quedando la tercia (4,6,7) en 5a col dentro del bloque 8; tercia (1,4,7) en 1a fila cuaterna (1,4,7,9) en 8a col quedando el #4 alineado en dicha col dentro del bloque 9 ent se formó el par (4,7) en 2a col dentro del bloque 7, así (7,2)=1; par (4,7) en 7a fila; se firmaron los pares (4,7) y (5,8) en 9a fila y éste dentro del bloque 9 ent (9,5)=6; tercia (1,6,9) en 8a fila dentro del bloque 9 ent (9,8)=4 (9,2)=7 (8,2)=4 (8,5)=7 (7,5)=4 (7,7)=7 (1,9)=7 (6,8)=7 (1,7)=4 (1,3)=1 (2,7)=3 (2,9)=8 (9,9)=5 (9,7)=8...

[@SudokuGuy]

Well done.

[@marialuisa4227]

Thank you 😊

[@SudokuGuy]

Thanks Maria. Please tell others about my site.

[@juliarenner7701]

Thank you so much for existing and doing what you do!! Just solved my hard sudoku with your help :) love from Austria (no kangaroos here)

[@SudokuGuy]

Wonderful! Congratulations Julia and thanks for your support. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@anandarao8942]

Very brilliant puzzle.. once 3 found.. game is easy..🙏

[@SudokuGuy]

Yes Ananda. congratulations and thanks for your support. Always something to learn eh!

[@anandarao8942]

@@SudokuGuy thank you for the reply sir..yes learning is continuous process 🙏🙏

[@virusgomati5180]

Great 😃👍

[@SudokuGuy]

Goodonya mate! thanks for your support. Robin

[@goaltheory]

I can do a hard sudoku in 30 minute because of this you! You are the best! And your enthusiasm is so high you always make my day! #SudokuGuy!

[@SudokuGuy]

Truish you have made my day. Thanks. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@davidwalters313]

Thanks very much. I expect you are going in the sea most days! Merry Christmas!

[@SudokuGuy]

Happy holidays!Not yet...too busy, but it is great to look at David. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@davidwalters313]

@@SudokuGuy will do!

[@kathleenrobbins7544]

Love the videos. I still don't understand the T formation. I'll have to study a little more!

[@SudokuGuy]

If you go Kathleen to my channel page sudokuguy.com you can find the t lesson in the advanced section. All the best.

[@alsh449]

it was great!

[@SudokuGuy]

Hi Amit. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@bluerizlagirl]

That flurry of activity at the beginning shows the advantage of only marking a candidate when it can go in one of exactly _two_ possible places; because as soon as you eliminate it from one of them, you know it _must_ be in the other one. And by chasing down all possible either-or pairs early on, you probably just end up creating new ones elsewhere later anyway as the grid gets filled in and possibilities disappear .....

[@SudokuGuy]

HI bluerizlagirl You are getting the idea. Well done. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@deanullerich1622]

When is your next Video? I have seen all of them and have a Word file summarizing them all. I have learned much from the previous 86!

[@SudokuGuy]

Hello Dean. My next video is being loaded next week. Go to the COMMUNITY TAB on my channel page to get details of the premier. Robin

[@peterkemp4372]

Have a great Christmas with your gang down under. All the best. Relax and enjoy. From us in the Bahamas.👍🥳🥳🥳🍷🍷🍷🍷

[@SudokuGuy]

Happy holidays! to you and enjoy the Bahamas. It is hot here now in Australia.

[@Honeyyboooo]

Hi sir, hope you are doing well. Today I watched a Drama called Navillera, and it reminded me of you. Keep going on your path, I am rooting for you!

[@SudokuGuy]

Thank you, I will Picky So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@Honeyyboooo]

@@SudokuGuy for sure! I will hopefully get better at sudoku too, thanks for the reply!

[@aleksandartonev8472]

just wanna say 22 year old here enjoying the sudoku channel +1 respect from me🍺

[@SudokuGuy]

Thanks Aleksandar. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@jbxyzmnp8444]

The best solution ever for me a beggener

[@SudokuGuy]

Thanks JBxyzmnp. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@Guille-g8l]

When will you upload your next tutorial?

[@SudokuGuy]

ASAP I am waiting for mu famous white board to arrive from Canada. It has taken over 7 months due to covid ETC. There are over 140 videos to look at in the meantime. Go to sudokuguy.com and click on videos to see a list. Happy new year.

[@lordxabbu]

Took me 17.5 minutes. I would say 4 out of 10 for difficulty. A nice starter puzzle.

[@SudokuGuy]

Yes. and that is why I suggested in my description that it was for beginners as well.

[@AnonimityAssured]

I have to say that I'm astounded at how easy that was. The solution just unfolded like a flower in the morning (59 = row 5 column 9): 59, 42, 79, 38, 16, 55, 53, 32, 21, 62, 12, 63, 61, 41, 51, 31, 91, 72, 54, 44, 58, 48, 56, 24, 66, 64, 34, 27, 74, 14, 26, 75, 77, 76, 45, 46, 29, 19, 68, 98, 82, 92, 85, 86, 93, 83, 96, 86, 97, 99, 37, 25, 35, 17, 33, 23, 13, 28, 89, 87, 88, 67, 39, 69. I suppose I could say I was lucky, in that it perfectly suited my scanning style.

[@SudokuGuy]

Congratulations Julian. Happy New Year.

[@AnonimityAssured]

@@SudokuGuy Thank you, and a Happy New Year to you. Also, thank you for this gem of a Sudoku.

[@Rebekah347]

Have you ever considered teaching about KenKen puzzles, Sodukos that include mathematical equations?

[@SudokuGuy]

Thanks R for your question , sorry I am so busy just looking after my sudokuguy site at present.

[@stonebreaker3555]

It looks like he is on his Mac. I like the computer program he is showing us. Please let me know the name of the program he is using that he is using in the video.

[@SudokuGuy]

Go to channel page Under video click on SHOW MORE

[@KarenDixon-gd2gn]

Am enjoying this game

[@SudokuGuy]

That's fantastic Karen . Lots to learn eh! So glad you found my site."the most popular site online to learn sudoku" Please share with others, subscribe and click the bell by the subscribe button. Have fun as you learn step by step how to solve. For a list of videos go here: kzbin.info/door/d8JaOdfEWcJOtwG6YayW0w sudokuguy.com

[@Andrew21882]

This was a very easy puzzle.

[@SudokuGuy]

Yes and yet it has only 17 numbers. Therefore small numbers of beginning numbers doesn't necessarily mean it is hard.

[@thomaswilke6312]

Where’s your famous sudoku white board? It’s so unusual to see you doing a puzzle without it

[@SudokuGuy]

If you read the description under the video Click on SHOW MORE you will note. that i have been waiting for months for it to arrive in Australia from Canada. It has now arrived and my recent video is on the white board (tutorial # 87) Thanks for your interest and support.

[@drewkerr5413]

If only it were that simple. The computer app might make it easier than scribbling with pencil on paper. But anyway it was very enjoyable. So thanks for that.

[@SudokuGuy]

Thank you so much 😀 Please tell others about my site. Master the easy puzzles first using my step by step method. Thanks for your support, and please tell others about my site. It is free! Robin

[@fernandapeixot]

Adoraria uma tradução em português...

[@SudokuGuy]

go to my channel page. kzbin.info/door/d8JaOdfEWcJOtwG6YayW0w Look for transaltion to your language video. Alll the best.

[@gie3222]

18:15 why 5 ??

[@SudokuGuy]

Glad to help but please tell me the time on the video you are referring to. This saves me time.

[@anthonyxuereb792]

More than about memory, it's more about the female mind and its capabilities (to be feared and respected) You're opening remarks about having more or less numbers is reassuring.

[@SudokuGuy]

Thanks.

[@ritakuyumjian7896]

🎉😊

[@SudokuGuy]

So glad you found my site."the most popular site online to learn sudoku" Please share with others, subscribe and click the bell by the subscribe button. Have fun as you learn step by step how to solve. For a list of videos go here: kzbin.info/door/d8JaOdfEWcJOtwG6YayW0w sudokuguy.com youtube.com@sudokuguy

[@sunilchaudhari970]

I solved n enjoyed being maths teacher

[@SudokuGuy]

You are good a logic.

[@sunilchaudhari970]

1st time i solved 17 known 64 unknown sudoku

[@SudokuGuy]

Congratulations.

[@guill3978]

Not every sudoku puzzle with 17 clues is easy. I have found one that is hard, therefore not every puzzles with 17 clues are solved in the same way.

[@SudokuGuy]

Correct.

[@kaylemoine1571]

Don't get too dependent on computer sudoku, like me. Have a hard time working puzzles on paper. Computer makes it too easy.

[@SudokuGuy]

I agree and finally my famous white has arrived and next tutorial I will be back to the white board.

[@indigobunting2431]

A good beginner sudoku. No tricks.

[@SudokuGuy]

Thanks you. All the best as you continue to do more advanced puzzles.

[@hermanmullings91]

I want to playa new ge

[@SudokuGuy]

Hello Herman Sorry I do not understand. to watch in your language go to kzbin.info/www/bejne/pZS8fZ-sp6-kgc0

[@bunty00]

Sir I want to send one query of xwing which gave me wrong.. So kindle send me whatsapp or email so i can send..

[@SudokuGuy]

Hi Mayur Send to [e-mail] Look at tutorial # 62 and 63 before sending.

[@1943sumrallgirl]

This new board confuses me. I can't keep up with what you are doing. Before, you went slow enough I could figure out why you were doing a particular thing. Your voice for some reason isn't as clear as it was before. I am new at thus and I am having a hard time keeping up with you.

[@SudokuGuy]

Sorry! My board was being shipped to Australia and I had to use this system only for a little while. If you go to my channel page you can see that I change back to the normal system (see below) This was a difficult puzzle. I hope you have looked at my channel page (see below) where I cover easier techniques. So glad you found my site."the most popular site online to learn sudoku" Please share with others, subscribe and click the bell by the subscribe button. Have fun as you learn step by step how to solve. For a list of videos go here: kzbin.info/door/d8JaOdfEWcJOtwG6YayW0w sudokuguy.com

[@VietPhan-is7qb]

De qua

[@SudokuGuy]

Hi Viet. Thank you for your support. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@phamminhtienshi7028]

123456789 Will is the right one?

[@SudokuGuy]

Sorry I need more information. So glad you found my site. “the most popular site online to learn sudoku” Please share with others, subscribe (FREE) and click the bell by the subscribe button. Have fun as you learn step by step to solve. You will find all of my videos below. sudokuguy.com kzbin.info

[@jo92414]

Within 3mins solved! Not hard.

[@SudokuGuy]

It goes to show that the number of initial numbers is not necessarily a sign of difficulty.

[@moddymeadow]

First view

[@SudokuGuy]

Hello ALL. I will be premiering tutorial #86 on Tues Dec 21 at 10.30am (Adelaide) my time. Check your time zone. The video is unique as I solve a puzzle with only 17 initial numbers. Most of these types of puzzles are hard BUT, I show that they can be solved with basic sudoku techniques. After the video I will be offering a LIVE STREAMING SEGMENT, when you can ask questions etc. kzbin.info/www/bejne/apbWoJewe5uDmdU