The hardness of the butter is proportional to the softness of the bread.

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## Photography Class - Answer

The pairs who were successful getting pictures were:

Perry and Quinn photographed the anteater.

Perry and Toby photographed the bear.

Rex and Scott photographed the crocodile.

Scott and Toby photographed the deer.

Quinn and Rex photographed the emu.

## Solution

There are ten possible pairs. Each person went out four times, each time with a different partner. Each person got a photograph twice and got nothing twice.

First, to determine which pairs photographed an animal and which didn't, make a 5x5 matrix with row and column headings of Perry, Quinn, Rex, Scott and Toby. Since we don't always know what animal was photographed, assign the animals a number, 1 through 5.

Everybody snapped two animals. So you can assign animal 2 to P [(P, RST) = 2] and you can assign animal 3 to Q [(Q, RST) = 3] in the matrix.

Then you are left with assigning animal 4 to S and animal 5 to T [(R, S) = 4 and (S, T) = 5.]

Since S has both animals 4 and 5, S cannot have animals 2 and 3. That means that we can assign 2 to R and 3 to T.

The pairs who were successful were (P, Q), (P, T), (Q, R), (R, S) and (S, T).

Next, we need to determine which pair photographed which animal. We know that

• The Emu is animal 1 or 3.
• The Anteater is not 2 and 5.
• The Bear is not 4 and 5. Therefore, the bear is 2 or 3.

Consider these cases separately: (Emu, Bear) = (1, 2), (1, 3) and (3, 2). The first two cases lead to contradictions. Therefore, (Emu, Bear) = (3, 2) which leads to Crocodile = 4.

Then, since Toby did not photograph the Anteater, the Anteater cannot be 2 or 5. So the Anteater must be 1.

Then the Deer is 5.

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