UPSC SCHOLARSHIP TEST CLASS | CUBES & DICE AND CODING & DECODING | SHANKAR SIR | TAF

Added: 2026-05-17

[00:00:00]Hello aspirants warm welcome to the session. Today we are going to see the topic of cubes and dice. First of all previous series of topics.

[00:00:16]One of the important topics is cubes and dice.

[00:00:30]Rubik's cubes 3x3 matrix 3x3 So 3x3 right six faces.

[00:01:17]different.

[00:01:36]How many cubes are having no side painted faces?

[00:01:42]Right. foreign.

[00:02:01]Face blue color. Blue face.

[00:02:18]Yellow.

[00:02:32]Right.

[00:02:35]Six faces.

[00:02:45]Six faces.

[00:02:56]Uh face corners.

[00:03:14]The corner points.

[00:03:23]Corners corners or else vertices right joining the two vertices or two corners it's called edge it's called edge so the vertices vertx Plain point total edges.

[00:04:29]Right.

[00:04:34]First of all 3x3 matrix I mean 3x3x 3 5x 5 7 by 7 cubes First basic properties.

[00:05:19]Next point we have to know that Normally saying the cube.

[00:06:32]thing.

[00:06:36]So cube on the Okay.

[00:06:57]So till the Last Right.

[00:07:36]Dimension three dimension yaxis and then x-axis ais Y axis X is Z X Y Z axis three dimension.

[00:08:29]Till the full slicing full slicing to the extent. The last point. Till the last till the last point.

[00:08:58]Say 3x3 matrix 3x3. 3x3 3x3 3x3 we are making 3x3 matrix cube 3x3 yaxis So 3x3 max meaning that 97 27 total values 27.

[00:10:17]So last three right? Okay.

[00:10:44]Number of cuts needed for to get a 5x matrix 5x cube from a solid cube 5.

[00:11:09]So number of cuts needed to to make an from solid individual entity from that we can get get into the smaller parts of 5x 7.

[00:11:26]Okay. Next of all faces are covered with same paint or else the total parts total faces are covered with different kind of distinct paintings. things.

[00:12:00]Right.

[00:12:28]Each cube have four cm forming framing of 20 cm.

[00:13:00]We have to make it into a side having 4 cm smaller cube.

[00:13:09]So larger, smaller.

[00:13:26]N value N is nothing but large side of cube by small side smaller Right. So total value.

[00:14:06]So 20 by small.

[00:14:35]same like that.

[00:14:39]Same understanding four x y and ais.

[00:14:50]So 12 cuts needed to find the she to get a 5x5 matrix of cube like 4 cm from a solid cube of 20 cm Right.

[00:15:12]basic understanding right.

[00:15:35]So proportional value, right?

[00:15:54]Yeah.

[00:16:22]Red.

[00:16:27]Three side Open to the faces.

[00:17:16]Right.

[00:17:18]Three side painted which is equal to number of corners or vertices meaning that Open side faced right two side painted two side.

[00:18:23]As simple as that.

[00:18:29]in the middle.

[00:18:33]Ed except the corner faces. Except the corner.

[00:18:57]US two side painted two side painted basic properties of Right.

[00:19:45]remaining we have to consider total we edges total of two side painted one One side exposed to the surface except the Each each individual entity One side square.

[00:21:11]So six faces. So zero side painted meaning that 3x3 values dimension 3D values three dimension XI nus N value saying the whole cube.

[00:22:49]Basic understanding objectives to the square n into n minus to the whole cube propert value.

[00:23:49]painted two single side rightcept is painted by green color and is then cut into a cubes of cubes of 1 cm cm.

[00:24:23]What are the total number of cubes which have zero surface painted?

[00:24:29]Zero surface painted after cutting the values.

[00:24:45]Okay.

[00:24:57]Right.

[00:25:00]Okay.

[00:25:23]Okay.

[00:25:41]Okay.

[00:25:46]Each cube side value would be 1 cm.

[00:26:05]Four cuts.

[00:26:10]1 1 2 3 4 1 2 3 4 till the last Y equal same value means all sides of values same 1 2 3 4 tell the values of last end point.

[00:27:12]Okay.

[00:27:20]Four So 5m 1.

[00:27:45]So 125 12.

[00:28:14]So, first of all, 1 2 3 4 5. So each over 3 zero surface zero surface 5 - 2 the whole 3 means 27 So 27 In the 3 + 3 last Moon 3 27 surface 27 surface, right?

[00:30:56]to the whole square to the whole square. 3 square 9 into 6 54 54 right cube and then cut into cubmid.

[00:31:40]What are the total number of cubes which have zero surface painted again? Zero surface painted.

[00:31:54]So large value small value.

[00:32:15]But the conceptual clarity but the conceptual understanding is same from the respect to the point of both questions Previous question number same like that n minus to the whole cube.

[00:32:50]So n would be five 5 - 2 the whole cube 3 cube same value 27 right a cube has all its faces painted with different colum different colors it is cut into a smaller cube of equal sizes such that the size of a smaller cube is 1/4 of the big cube value cm4 ratio.

[00:33:54]Okay sir.

[00:34:12]four cubes.

[00:34:24]Which means that it's a multiple of four, right? So small 14.

[00:34:55]So number of proportionat right as usual that Right.

[00:35:31]Okay. Then the number of small cubes with only one of the sides painted. So only one of the sides only one side painted.

[00:35:43]One side painted.

[00:35:48]NUS the whole square into six.

[00:35:54]Right. So total values 4 - 2 square into 6 2 4 into 6 2 4 into 6 24 1/4 of the Right.

[00:36:31]Okay.

[00:36:45]Projection point. The framing question what we have to get into that point the outer surface of 4 + 4 is painted completely red.

[00:37:12]It is sliced parallel to the faces to the 64 1 exact 64 mean 64.

[00:37:28]Okay. How many small cubes do not have painted faces?

[00:37:34]So same like this 4 by 4 by 1 is four zero side painted again nus to the whole cube.

[00:38:02]Okay.

[00:38:08]We know that fourus 2 cube which means that eight do not have painted faces. Right. Okay.

[00:38:33]Same like that you can able to do mind itself right ais y ais ais then it will make into smaller cube.

[00:39:18]Okay.

[00:39:23]of dimensions 3 length 7 x ais 7 y ais five is ais three okay painted red green black uh red green blue color on each pair of opposite faces of dimensions Each pair of opposite faces.

[00:39:57]Okay.

[00:40:00]Green. Sorry.

[00:40:08]Next values. I + 3 + 3, right?

[00:40:50]7 + 3 uh sorry 7 cm 5 cm in the value 3 cm 7.

[00:41:26]Okay.

[00:41:29]Then the cuboid is 5 + 3 5 7 5 right. Sorry. Okay.

[00:42:01]Then the cubad is cut and separated into various cubes each side each of side length 1 cm.

[00:42:13]Which of the following statement is correct? First of all, Each side of a cube having a 1 cm length each side.

[00:43:09]cubes over 1 2 3 4 5 6 7 cubes.

[00:43:41]last.

[00:43:50]Okay. Right.

[00:44:02]So cime foreign.

[00:44:32]And 3 4 5 cubes. 1 2 3 4 5 Cime.

[00:44:51]So, okay.

[00:44:59]Right.

[00:45:28]5 + 3 5 green 5 + 3 right 1 2 projection 1 2 3 4 Okay.

[00:46:13]over each cube having a side of 1 cm from the having a cube cuboid values from the cube also 7 five and three exactly there are exactly 15 small cubes with no paint on any face no paint on any face 15 small cubes Zero painted nus to the whole cube. Zero side to the whole cube here.

[00:47:12]over 7 mip Nus 7 So 5 - 2 and then 3 by 1.

[00:48:12]So 7 - 5 5 - 2 3 3 - 1 15. Yes, exactly.

[00:48:19]15 having a zero set.

[00:48:26]15 cubes.

[00:48:42]in the point total.

[00:49:04]So Outside Right. Projection.

[00:49:39]Fore 1 2 3 4 5 1 2 3 into 5.

[00:50:02]So 3 into 5 15.

[00:50:07]So conceptual clarity single.

[00:50:30]Okay.

[00:50:35]By the way, there are exactly six small cubes with exactly two faces.

[00:50:55]face.

[00:50:57]Six small blue.

[00:51:07]Blue and green.

[00:51:34]Exactly.

[00:51:36]Exactly.

[00:51:55]Four cubes only having a two side faces painted. Two faces painted in a combination of blue and green.

[00:52:03]So four cubes only painted with blue and green.

[00:52:31]So one only position.

[00:53:05]Right. Okay.

[00:53:08]So, dice. Dice.

[00:53:39]Right. So one opposite normal standard.

[00:54:08]Okay.

[00:54:12]Same.

[00:54:24]for symbol Right.

[00:54:54]sides.

[00:55:00]Four adjent sides.

[00:55:10]The front face.

[00:55:27]The yellow the blue face red blueent.

[00:56:02]Right.

[00:56:08]Opposite side.

[00:56:47]in a standardize a side having a value of a single dot. So what would be the opposite side of that value? An opposite value having a how many dots? Standard face.

[00:57:28]So side opposite Okay.

[00:57:55]Having a value of single dot. What would be the opposite values having a how many dots single?

[00:58:09]Right sir. Okay sir. Standard.

[00:58:40]See one one side having a common common face common value or nearby 4 comma 3 2a 6 2 common value.

[00:59:48]direct opposite First one projection. First projection.

[01:00:33]First clockwise clockwise clockwise or anticlockwise 4 5 4 3 The same manner.

[01:01:03]Five 26 2 opposite opposite faces and then three opposite.

[01:01:38]Not only that exactly we can able to get that 53 52 right 3 4 5 6 2 anticlockwise clockwise clockwise rotation rotation four opposite right single common okay Two sides are common.

[01:03:04]5 2 3 5 2 One projection projection.

[01:03:32]saying 1, right? Either either either two or four I mean either four or six four or six or Five.

[01:04:24]Suppose in the case of line rotated positions of a single solid are shown below. The various faces of the solid are marked with the different symbols like dots, cross and line.

[01:04:46]answer the three items that follow the given figures.

[01:05:00]What is the symbol symbol on the face opposite to the containing a single single single dot dot from basis of one and two from basis of on basis of see on basis of one and two we can able to reduce that uh single opposite single opposite Okay.

[01:06:06]Two.

[01:06:10]Okay. Two.

[01:06:13]Single.

[01:06:15]Single. Two.

[01:06:20]One single dot and two dot. Single and two dot. One from one and four. We can able to tell that two line crossite opposite either opposite Six places 2.2 four 2.2 two four from two and three and three from two and three four. Okay.

[01:07:51]Right.

[01:07:58]Three.

[01:08:03]What is the symbolite containing two dots? Two dots.

[01:08:13]Four dots.

[01:08:15]crossite line.

[01:08:19]Okay. Right.

[01:08:22]So my Uh state each of the six different faces of a cube having has been quoted with different colors.

[01:09:06]V.

[01:09:08]Okay. Following information is given colors Y B or adjacent faces.

[01:09:21]Which is the color of the face opposite to the face with the statement.

[01:10:09]So value Yellow, orange.

[01:10:41]And then G already.

[01:11:07]foreign.

[01:11:20]for B.

[01:11:59]Okay. Ve saying.

[01:12:23]So total values Next.

[01:13:00]Gee, G.

[01:13:14]So opposite V saying I Vite So relative relative in a concept manner we have to we can able to deduce that Right. So unfold And waiting now.

[01:14:36]So values 1 2 3 4 5 6. Right.

[01:15:03]top right. So total valositech.

[01:15:55]Oh, so values.

[01:16:44]Absolutely.

[01:16:58]concept understand right opposite saying Top in or correct formation of dice.

[01:18:20]An explanary figure of dice is given.

[01:18:24]Figure of dice is given unfold.

[01:18:29]Study the figure and identify the correct dice formed by the figure.

[01:19:01]option we have left with D option 1 three and then four opposite sides conditions We can directly go with the fourth option as prescribed right values right decoding for WhatsApp.

[01:20:10]decryption decryption.

[01:20:22]You know that one number postal code number TN6 val series.

[01:21:18]concept.

[01:21:38]Coding, decoding.

[01:21:47]5 10 15.

[01:21:54]So previous for Chinese language.

[01:22:27]Chinese language 24 is equal to water is colorless in a certain code language pen is written as 35 language 35 Char is written as 39.

[01:23:17]Squares.

[01:23:39]Obviously, we can go with 35.

[01:23:51]35 QR 14.

[01:24:01]Okay.

[01:24:04]So obvious C h a i r see. So, so uh 9 18.

[01:24:46]So, 39. So, table.

[01:25:03]So, T A B L E 20.

[01:25:22]21 23 23 + 12 35 40 35 + 5 40 table right the letters from A to Z are numbered from 1 to 26 respectively Okay.

[01:25:53]Gi= 1578.

[01:25:57]G H I G H I G HI 15 78 15 D E F 92 D E F 9 on two sing F 5 So double double the value Right.

[01:27:26]ABC.

[01:27:30]So, ABC 1 2 3 2 4 6 2 4 6 2 4 6 2 4 Z is written as C H U R Then how is player is return? player is return.

[01:28:13]T H U 26 5 18 15 C value 8 21 18 loop 18 + 3 21 15 + 3 18 18 Z is written as then how is player written a Y pl A Y E R. So valu for saying SH 21 su b.

[01:30:12]Okay.

[01:30:15]Okay.

[01:30:19]Okay, we are able to deduce that certain code sand is udg sand udqg and bird is ug then what is the code for sand udg 2D QG.

[01:30:52]Okay.

[01:30:56]Bird is E U bird.

[01:31:05]E L U G L O V.

[01:31:19]U 14 M 14 M 13 QR O Q value G value.

[01:31:53]Okay. So, but right + 3 + 3 14.

[01:32:30]Okay.

[01:32:44]33ist.

[01:33:02]Okay.

[01:33:21]S U V + 3 L + 3 Okay.

[01:33:53]H Y H Okay.

[01:34:13]Military code with system is near.

[01:34:29]System system nearer. N E A R E R N E A nearer. R E R.

[01:35:01]A E N E R A E N.

[01:35:06]A E N R E R.

[01:35:13]Uh fraction fraction.

[01:35:24]fraction.

[01:35:43]scramble.

[01:35:50]S Y the Y in the moon.

[01:36:07]R E first. C A R F I c a rf c a rf.

[01:36:44]Yes, exactly.

[01:36:58]T in the last certain code Shivans is written as Shiva Shivans then how will Ankita will be written in the code let's take it as a homework 256 means red color chalk question.

[01:38:10]Starting on the word 256 Now sign 2 5 6 red color 589 means green color flower. 589 589 means green color flower 254 means white color chalk. 254 means white color chalk, right?

[01:39:34]The digit in the code that indicates white.

[01:39:54]White. First, first By the way, four obvious for Right.

[01:41:31]8 N Right. Same like this.

[01:42:15]Either green either or flowers or eight cannot be either either or optional concrete whatever Whatever statement whatever value n option A n option B eight option C number four option D none of this none of this can have no other clues or ideas we can go for cannot be determined or else none of these or else either okay or okay right in a certain code language in a certain code language How many goals scored is written as 4397? Many more matches is written as 982 and he scored five is written as 163.

[01:43:57]How is goals written in that code language?

[01:44:06]How many goals scored?

[01:44:09]How many How many how many goals go? How many goals scored?

[01:44:21]Excuse 4397.

[01:44:27]43 97.

[01:44:31]Uh, many more matches. 982.

[01:44:35]How many?

[01:44:38]How many more?

[01:44:42]Many more matches.

[01:44:45]982, right?

[01:44:57]He scored five. He scored five 163.

[01:45:05]He scored.

[01:45:09]He scored five 1 six.

[01:45:18]How is many First comparative for repeat.

[01:46:28]So goals scored.

[01:47:03]Either four or seven.

[01:47:07]Either four or seven.

[01:47:11]Four or seven. Suppose in the option we have to go for none of this.

[01:47:16]Seven more option. C option none of this exact same Right.

[01:47:44]472 right is written as 1 2 3 4 5 and as 675 849 ramen R A R A M O N 1 2 3 4 5 1 2 3 4 5 D 675 time.

[01:49:07]Okay.

[01:49:12]Right.

[01:49:14]675849 explain 675 849.

[01:49:31]What will be the ham value?

[01:49:36]A.M.

[01:49:54]time exact.

[01:50:17]value.

[01:50:21]position.

[01:50:33]We can able to right. We can able to tell that again.

[01:50:52]9 23 23 93 23.

[01:51:03]Okay.

[01:51:08]Right.

[01:51:10]LSJ XVC saying LSJ LSJ XVC is the code for Mumbai Mumbai LSJVC LSG XVC. Okay. For Mumbai first Mumbai code LSJ XVC LSJV right?

[01:51:51]What is the code for Delhi Fore 12 U ST UV T1 ST value again 13 J value one - 2 - 3 2 X U V sorry X X X Y Z 24 so minus 4 U V So - 6 same like that same - C D minus 2 again I CCI uh -4 D - 5 again D right CCI D -1 - 2 -3 -4 - 5 - 4. Okay.

[01:54:33]So 4 - 1 3 5 - 2 3 uh 9 12 - 3 9 8 - 4 4 9 - 5 again four saying CCA DDR first.

[01:54:56]So okay let's take what is the missing term in the following Right. Same like that.

[01:55:34]This is also take as an homework df.

[01:55:46]Then what is the value of the x? Is it ud? Yes.

[01:55:52]Okay. Right.

[01:55:56]Same.

[01:56:00]This is also take it as some homework.

[01:56:21]If every alternative letter of the English alphabet from B onwards including B from B onwards including Lower Dain.

[01:57:06]Okay.

[01:57:10]Alternative even small 26 68 lower.

[01:57:41]Other than that, other than that even odd positions 1 3 57 meaning that from the including 37 37 3.

[01:58:18]Okay. The remaining letters are capitalized. Then how is the first month of the second half of the year is written? First month of second half of the year 6 months. 6 months. First off, last month June. Second month, July. Second, first month of second.

[01:58:47]Right.

[01:58:53]Jul.

[01:59:21]So J small upper small upper case small upper small upper case in a certain code language bicycle is written as FM D uh JC Then laptop is will be same like Rain is called as 5831.

[02:00:26]What is for wanted? Wanted rain 58 31.

[02:00:48]Water is quoted as 48625.

[02:00:56]486 25 date is coded as 7862.

[02:01:05]Date 7862.

[02:01:13]What will be the code for wanted?

[02:01:25]First of all, again.

[02:01:52]T6 W 48 481 Right.

[02:02:25]T again 481627 language poly is written as it use MPQ.

[02:02:58]ide.

[02:03:14]So meaning that we can able to identify the values exam point of The letters A to Z are numbered from 1 to 26. If ABC is ABC is 14, D F is 77. Then what is G hi equal to ABC 14?

[02:04:04]ABC 14 D F is 77 D E F 77 G Right. So 1 2 3 1 2 3 4 5 6 minimum 7 starting Function 1 into 2 into 3 6 4 into 5 into 6 20 12 square pattern.

[02:05:44]four square 16 5 square 25 square 36.

[02:05:57]Okay. Exact right.

[02:06:01]So, GI, GI value 7 8 9 7 4 + 64 + 81. So, 194.

[02:06:33]Okay.

[02:06:45]Okay.

[02:06:54]Right.

[02:07:01]If the order of the letters in the English alphabet is reversed and each letter represents the represents the letter whose position it occupies, then which of the following represents Loab Alphabet series 1 to 26.

[02:07:43]Last final option.

[02:07:56]A B C D I, J, K, L, M, N.

[02:08:18]1 2 3.

[02:08:31]So normal for I mean Previous series, right?

[02:09:05]L U C where L U K L L U C K Cosite X Kosite P value D FX PLD Left rightward left Right. 27.

[02:10:46]T U S T U V U 21.

[02:11:05]X 14 14 15 W. We know that U V W 23 27 Without using without using the letters corresponding values we can able to deduce in the format of understanding the concept from the previous sess right?

[02:12:11]Right.

[02:12:19]I hope that this session is very helpful for your exam preparation. Kindly do more practices time taken to solve the questions in each individual it will gain your the overall attempt score value saying we will see in the next session. Thanking you.