#Can someone pls help me solve this question pls

72 messages · Page 1 of 1 (latest)

raw depotBOT
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hybrid cloak
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<@&1309522179368419349> i don't know where to start

patent parcel
hybrid cloak
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Congruent to 0

patent parcel
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So then you want 7^a + 7^b + 7^c + 7^d == 0 (mod 100).

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Now, what are the possible values of a digit?

hybrid cloak
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{1,2,...,9}

patent parcel
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Almost.

hybrid cloak
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0

patent parcel
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So then just check what those powers of 7 are mod 100

hybrid cloak
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manually?

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just calculate them?

patent parcel
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It's not actually that bad.

hybrid cloak
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kk

patent parcel
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You'll notice something halfway through.

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Less than halfway through.

hybrid cloak
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how long is halfway

patent parcel
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...how long is... halfway through... 0-9...

hybrid cloak
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kk

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i'll lyk when im done

patent parcel
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Ping me.

hybrid cloak
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by the way

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can you help me with the proof q

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pls

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🙏

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i've been stuck for ages

patent parcel
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...which "proof q"?

hybrid cloak
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There are fourteen rectangular tiles with sides of length 3 and 4 and one square tile with sides of length 1 to tile a square floor which is 13 by 13. (a) Show that this is possible if the 3 by 4 tiles are cut into two 3-4-5 triangles. (b) Prove that this is impossible without cutting any tiles.

patent parcel
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New problem, new thread.

hybrid cloak
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sure

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ty

hybrid cloak
patent parcel
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Let's finish this one first.

hybrid cloak
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👍

hybrid cloak
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pattern

patent parcel
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What do you see?

hybrid cloak
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1

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7

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49

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43

patent parcel
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Right.

hybrid cloak
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.
.
.

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we need to find the max number of sol?

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right?

patent parcel
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Right.

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Notice that our powers of 7 come in pairs.

hybrid cloak
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wait

hybrid cloak
patent parcel
hybrid cloak
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no

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umm

patent parcel
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Is division defined in modular arithmetic?

hybrid cloak
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wait nvm what am i talking abt 😭

patent parcel
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Look at your list of four possible values.

hybrid cloak
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now we need to find the combinations of four numbers from 1,7,49,43 that are divisible by 100

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@patent parcel

patent parcel
hybrid cloak
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I got 36

hybrid cloak
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I just looked at their last digits

patent parcel
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...in particular, they come in pairs that sum to 50.

hybrid cloak
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ye ig

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is this correct/

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?

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@patent parcel

patent parcel
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Honestly, it's late for me.

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I can pick this up sometime tomorrow maybe.

boreal siloBOT
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@hybrid cloak

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